For the physician Philinus of Cos Philinus of Cos lang el 3rd century BC , son of Hegepolis, was an ancient Greek athlete and five times Ancient Olympic Games Olympic winner. ref name golden Mark Golden, 2004 , Sport in the ancient world from A to Z , page 133. Routledge ref Career He was a five times Olympic winner in the Stadion ancient sports stadion and Diaulos running race diaulos running races akin to the 200m and 400m sprints of modern Olympics . His first victory came during the 128th Olympiad in 268 BC where, at the age of 14, he won the stadion race. From then he reigned for over a decade in the stadia of Ancient Greece. In the 129th Olympiad in 264 BC he won in both the stadion and the diaulos he repeated the feat at the 130th Olympiad in 260 BC where he also won in both the stadion and the diaulos. Besides the Olympic games he had a total of 11 wins in the Isthmian games , four wins at the Pythian games , and another four wins at the Nemean games . ref name golden In total he was victorious 24 times. Literary mention He appears in a poem by Theocritus , and is also mentioned by the geographer Pausanias geographer Pausanias and Eusebius . ref Theocritus, ii. 115 Pausanias, vi. 17.2 Eusebius, Chronicon , i. 207 ref Notes reflist Category 3rd century BC Greek people Category Ancient Greek runners Category Ancient Olympic competitors Category Ancient Pythian athletes el ... more details
Infobox station name Cos Cob style MNRR New Haven Connecticut image GreenwichCTCosCobRRsta09092007.jpg image size image caption East side of the station house address 1 Station Drive, br Cos Cob, CT 06807 2736 coordinates coord 41.03123 73.598313 type railwaystation region US CT display inline,title line Rail color box system MNRR line New Haven other platform 2 side platform s tracks 4 electrified 12,500 volt V Alternating current AC overhead catenary parking 567 spaces bicycle opened December 25, 1848 rebuilt 1890 ADA code owned zone services s rail title MNRR s line system MNRR line New Haven previous Greenwich next Riverside type2 All passengers 215,020 ref Using 260 weekdays in a year multiplied by number of weekday passengers 827 ref pass year 2006 pass percent 0 nrhp Infobox nrhp name Cos Cob Railroad Station embed yes image caption location Greenwich, Connecticut , United States USA lat degrees 41 lat minutes 1 lat seconds 52 lat direction N long degrees 73 long minutes 35 long ... added August 28, 1989 refnum 89000928 governing body The Cos Cob Metro North Railroad station serves the residents of the Cos Cob, Connecticut Cos Cob area of Greenwich, Connecticut , via the New Haven Line . Cos Cob is convert 29.6 mi km from Grand Central Terminal . The station has 567 parking ... Places in 1989 as Cos Cob Railroad Station . ref name nrhpinv3 cite web url http pdfhost.focus.nps.gov docs NRHP Text 89000928.pdf title National Register of Historic Places Registration Cos Cob ... the Cos Cob Bridge, thereby supplying the last link needed to complete the railroad from New Haven ... Sentinel and a guest on the first trial run, wrote The train had to remain at Cos Cob Bridge ... mnr stations station detail.cfm?key 220 Metro North Railroad Cos Cob http as0.mta.info mnr mstations ... from MTA http www.ct.gov dotinfo lib dotinfo ctgov Cos Cob.pdf Condition Inspection for the Cos ... of Historic Places Registered Historic Places DEFAULTSORT Cos Cob Metro North Station Category Metro ... more details
Orphan date February 2009 Od n de Buen y del Cos 1863 in Zuera , Zaragoza Province , Aragon , Spain &ndash 1945 in Mexico City was a Spain Spanish naturalist, politician and publicist. He founded the Spanish Institute of Oceanography , and was a senator and council member in Barcelona . Born to a tailor, de Buen studied Natural History in Madrid and Zaragoza. He became interested in oceanography after doing research on board of the Blanca fragatta. From 1889 to 1911 he taught zoology and botany at the University of Barcelona . On board of the Averroes , he studied the currents by Gibraltar . The acclimation of the Gambusia affinis , a larva eating fish used to combat malaria is attributed to his son, parasitology parasitologist Sad de Buen Lozano. In 1939, like many scientists, artists and intellectuals, he left Spain for Mexico in the aftermath of the Spanish Civil War . He died in Mexico City in 1945. Publications De Kristiania a Tuggurt 1887 External links es icon http www.ub.es geocrit b3w 542.htm Biography Persondata Metadata see Wikipedia Persondata . NAME Buen y del Cos, Odon de ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1863 PLACE OF BIRTH DATE OF DEATH 1945 PLACE OF DEATH DEFAULTSORT Buen y del Cos, Odon de Category 1863 births Category 1945 deaths Category People from Zaragoza comarca Category Spanish scientists Category Members of the Spanish Senate Spain scientist stub ca Od n de Buen y del Cos es Od n de Buen ... more details
Jos Mar a Rodr guez y Cos was a Mexico Mexican writer who promoted Positivism in the country. He was born in Tulancingo , Hidalgo state Hidalgo , Mexico in 1823, and although he began his studied to be a doctor, he had to leave university due to finances. He worked as a teacher and began to write, and became associated with Positivist writers such as Vicente Hugo Alcar z and Manuel Guill n . His master work is considered to be epic poem El An huac , published in 1852. Another popular poem is La Revoluci n francesa . He also wrote plays such as the opera Cuauht moc and translated a number of plays and other works from French and Italian into Spanish. Rodr guez y Cos died in Mexico City in 1899. ref name rincones cite book editor1 first Victor Manuel editor1 last Jimenez Gonzalez title Hidalgo Gu a para descubrir los encantos del estado trans title Hidalgo Guide to discover the charms of the state year 2010 publisher Editorial Oc ano de Mexico SA de CV location Mexico City language Spanish isbn 978 607 400 319 2 page 15 ref References reflist Category Mexican writers ... more details
Lists of United Kingdom locations Cos Cou Lists of United Kingdom locations header TOC clear Cos Lists of United Kingdom locations table header class vcard class fn org Cosby, Leicestershire Cosby class adr span class region Leicestershire span class note coord 52.55 N 01.20 W region GB type city class note gbmappingsmall SP5495 class vcard class fn org Coscote class adr span class region Oxfordshire span class note coord 51.58 N 01.26 W region GB type city class note gbmappingsmall SU5188 class vcard class fn org Coseley class adr span class region Dudley span class note coord 52.54 N 02.08 W region GB type city class note gbmappingsmall SO9494 class vcard class fn org Cosford, Warwickshire Cosford class adr span class region Warwickshire span class note coord 52.40 N 01.28 W region GB type city class note gbmappingsmall SP4979 class vcard class fn org Cosgrove, Northamptonshire Cosgrove class adr span class region Northamptonshire span class note coord 52.07 N 00.84 W region GB type city class note gbmappingsmall SP7942 class vcard class fn org Cosham class adr span class region City of Portsmouth span class note coord 50.84 N 01.06 W region GB type city class note gbmappingsmall SU6605 class vcard class fn org Coshandrochaid class adr span class region Argyll and Bute span class note coord 55.97 N 05.68 W region GB type city class note gbmappingsmall NR7082 class vcard class fn org Cosheston class adr span class region Pembrokeshire span class note coord 51.69 N 04.89 W region GB type city class note gbmappingsmall SN0003 class vcard class fn org Cosmeston class adr span class region The Vale Of Glamorgan span class note coord 51.41 N 03.18 W region GB type city class note gbmappingsmall ST1869 class vcard class fn org Cosmore class adr span class region Dorset span class note coord 50.84 N 02.47 W region GB type city class note gbmappingsmall ST6705 class vcard class fn org Cossall class adr span class region Nottinghamshire span class note coord 52.97 N 01.28 W ... more details
Cos 1 , cos sup &minus 1 sup or cos 1 may refer to cos sup &minus 1 sup or arccos , an inverse trigonometric function of cosine Cos 1 , one of two commonly used COS cells COS cell lines disamb ... more details
with trilinears math cos A cos B cos C math and the orthocenter with trilinears math sec A sec B sec C cos B cos C cos C cos A cos A cos B math , every point on the Euler line, except the orthocenter, is given as math cos A t cos B cos C cos B t cos C cos A cos C t cos A cos B , math for some t . Examples centroid math cos A cos B cos C cos B cos C cos A cos C cos A cos B math nine point center math cos A 2 cos B cos C cos B 2 cos C cos A cos C 2 cos A cos B math De Longchamps point math cos A cos B cos C cos B cos C cos A cos C cos A cos B math Euler infinity point math cos A 2 cos B cos C cos B 2 cos C cos A cos C 2 cos A cos B math References cite journal author Euler, Leonhard authorlink ... more details
if and only if P is a triangle center is the point given in trilinear coordinates by ap p q cos C p r cos B bq q r cos A q p cos C cr r p cos B r q cos A . Another theorem about the pedal triangle ... more details
multiple issues unreferenced October 2011 Image Law of haversines.svg right thumb Spherical triangle In spherical trigonometry , the half side formula relates the angles and lengths of the sides of spherical triangle s, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles. Formulas math begin align tan left frac a 2 right & R cos S alpha 8pt tan left frac b 2 right & R cos S beta 8pt tan left frac c 2 right & R cos S gamma end align math where a , b , c are the lengths of the sides respectively opposite &alpha , &beta , &gamma , math S frac 1 2 alpha beta gamma math is half the sum of the angles, and math R sqrt frac cos S cos S alpha cos S beta cos S gamma . math The three formulas are really the same formula, with the names of the variables permuted. See also Spherical law of cosines Category Spherical trigonometry ru ... more details
earth pressure is expressed as P sub a sub K sub a sub w h where math K a cos beta frac cos beta left cos 2 beta cos 2 phi right 1 2 cos beta left cos 2 beta cos 2 phi right 1 2 math where K sub a sub ... more details
lowercase de Longchamps point Image deLongchamps Point.svg thumb right The orthocenter H reflected about the circumcenter O gives the de Longchamps point L . In geometry , the de Longchamps point of a triangle is the reflection mathematics reflection of its orthocenter about its circumcenter . ref name mathworld Weisstein, Eric W. de Longchamps Point. From MathWorld A Wolfram Web Resource. http mathworld.wolfram.com deLongchampsPoint.html ref It is listed as X 20 in the Encyclopedia of Triangle Centers . Its trilinear coordinates are math displaystyle cos A cos B cos C cos B cos C cos A cos C cos A cos B math The point is Line geometry collinear with the orthocenter and circumcenter. ref name mathworld mathworld urlname deLongchampsPoint title de Longchamps Point ref See also Circumcircle Excircle Incircle Notes reflist geometry stub Category Triangle centers ar de Longchamps Punkt it Punto di de Longchamps nl Punt van De Longchamps ja ... more details
as math left x cos theta y sin theta, x sin theta y cos theta right math on the rotated ... x prime , y prime right math , then it is denoted as math left x prime cos theta y prime sin theta, x prime sin theta y prime cos theta right math on the un rotated xy coordinate system. Elimination ... is rotated by a quantity math theta math , hence math A left x prime cos theta y prime sin theta right 2 B left x prime cos theta y prime sin theta right left x prime sin theta y prime cos theta right C left x prime sin theta y prime cos theta right 2 math math D left x prime cos theta y prime sin theta right E left x prime sin theta y prime cos theta right F 0 math Expanding, the equation becomes math A x prime 2 cos 2 theta 2Ax prime y prime sin theta cos theta A y prime 2 sin 2 theta B x prime 2 sin theta cos theta Bx prime y prime cos 2 theta math math Bx prime y prime sin 2 theta B y prime 2 sin theta cos theta C x prime 2 sin 2 theta 2Cx prime y prime sin theta cos theta C y prime 2 cos 2 theta math math Dx prime cos theta Dy prime sin theta Ex prime sin theta Ey prime cos theta F 0 math Collecting like terms, math x prime 2 left A cos 2 theta B sin theta cos theta C sin 2 theta right x prime y prime left B left cos 2 theta sin 2 theta right 2 left A C right left sin theta cos theta right right math math y prime 2 left A sin 2 theta B sin theta cos theta C cos 2 theta right x prime left D cos theta E sin theta right math math y prime left D sin theta E cos theta right .... If math A C neq 0 math math begin matrix B left cos 2 theta sin 2 theta right 2 left A C right sin theta cos theta & & 0 B cos 2 theta left A C right sin 2 theta & & 0 B cos 2 theta & & left A C right sin 2 theta cos 2 theta & & frac left A C right sin 2 theta B cot 2 theta & & frac A C B end matrix math If math A C 0 math math begin matrix B left cos 2 theta sin 2 theta right & & 0 B cos 2 theta ... more details
hat a hat b hat c end bmatrix begin bmatrix a & b cos gamma & c cos beta 0 & b sin gamma & c frac cos alpha cos beta cos gamma sin gamma 0 & 0 & c frac v sin gamma end bmatrix begin bmatrix hat ... v sqrt 1 cos 2 alpha cos 2 beta cos 2 gamma 2 cos alpha cos beta cos gamma math For the special case ... x a ,x frac c ,z frac , cos beta math math y b ,y frac math math z c ,z frac , sin beta math Conversion ... math mathbf begin bmatrix hat x hat y hat z end bmatrix begin bmatrix frac 1 a & frac cos gamma a sin gamma & frac cos alpha cos gamma cos beta av sin gamma 0 & frac 1 b sin gamma & frac cos beta cos gamma cos alpha bv sin gamma 0 & 0 & frac sin gamma cv end bmatrix begin bmatrix hat a hat ... more details
Pat Delaney may refer to Pat Delaney actor , actress in Cos TV series Cos Pat Delaney Offaly hurler born 1954 , Offaly hurler Pat Delaney Kilkenny hurler born 1944 , Kilkenny hurler Patrick Delany New Jersey politician born 1969 See also Patrick Delany disambiguation hndis Delaney, Pat ... more details
mathrm hypotenuse frac a h math math cos theta frac mathrm adjacent mathrm hypotenuse frac b h ... hypotenuse right left frac mathrm adjacent mathrm hypotenuse right frac sin theta cos theta . math math cot theta frac cos theta sin theta . math math cot theta frac mathrm adjacent mathrm opposite ... frac 1 tan theta . math math sec theta frac 1 cos theta math math csc theta frac 1 sin theta math ... cos theta math math cos left pi 2 theta right sin theta math math tan left pi 2 theta right cot theta ... math csc left pi 2 theta right sec theta math Pythagorean identities Identity 1 math sin 2 x cos 2 ... theorem . math sin 2 x cos 2 x frac a 2 h 2 frac b 2 h 2 frac a 2 b 2 h 2 frac h 2 h 2 1. , math ... sides of math sin 2 x cos 2 x 1 math by math cos 2 x math for the second, divide by math sin 2 x ... 2 sin x cdot cos x 2 sin x cdot cos x 0 math Integrating this shows that the original identity is equal ... math math OP 1 , math math PQ sin beta , math math OQ cos beta , math math frac AQ OQ sin alpha , math , so math AQ sin alpha cos beta , math math frac PR PQ cos alpha , math , so math PR cos alpha sin beta , math math sin alpha beta PB RB PR AQ PR sin alpha cos beta cos alpha sin beta , math By substituting ... , we also get math sin alpha beta sin alpha cos beta cos alpha sin beta , math math sin alpha beta sin alpha cos beta cos alpha sin beta , math Another simple proof can be given using Euler s formula known from complex analysis Euler s formula is math e i varphi cos varphi i sin varphi math Although ... that for angles math alpha math and math beta math we have math e i alpha beta cos alpha beta i sin ... i alpha e i beta cos alpha i sin alpha cos beta i sin beta math Evaluating the product math e i alpha beta cos alpha cos beta sin alpha sin beta i sin alpha cos beta sin beta cos alpha math This will only .... Hence we get math cos alpha beta cos alpha cos beta sin alpha sin beta math math sin alpha beta sin alpha cos beta sin beta cos alpha math Cosine Using the figure above, math OP 1 , math math PQ ... more details
r B 1 r 1 B 1 r theta C 1 r 3 D 1 r ln r right cos theta & left E 1 r F 1 r 1 F 1 r theta G 1 r 3 H 1 r ln r right sin theta & sum n 2 infty left A n r n B n r n C n r n 2 D n r n 2 right cos n theta ... math A 1 r cos theta , math and math E 1 r sin theta , math define a trivial null state of stress ... math 0 math math r 3 cos theta , math math 2 r cos theta , math math 2 r sin theta , math math 6 r cos theta , math math r theta cos theta , math math 2 r 1 sin theta , math math 0 math math 0 math math r ln r cos theta , math math r 1 cos theta , math math r 1 sin theta , math math r 1 cos theta , math math r 1 cos theta , math math 2 r 3 cos theta , math math 2 r 3 sin theta , math math 2 r 3 cos theta , math math r 3 sin theta , math math 2 r sin theta , math math 2 r cos theta , math math 6 r sin theta , math math r theta sin theta , math math 2 r 1 cos theta , math math 0 math math 0 math math r ln r sin theta , math math r 1 sin theta , math math r 1 cos theta , math math r 1 sin theta , math math r 1 sin theta , math math 2 r 3 sin theta , math math 2 r 3 cos theta , math math 2 r 3 sin theta , math math r n 2 cos n theta , math math n 1 n 2 r n cos n theta , math math n n 1 r n sin n theta , math math n 1 n 2 r n cos n theta , math math r n 2 cos n theta , math math n 2 n 1 r n cos n theta , math math n n 1 r n sin n theta , math math n 1 n 2 r n cos n theta math math r n cos n theta , math math n n 1 r n 2 cos n theta , math math n n 1 r n 2 sin n theta , math math n n 1 r n 2 cos n theta , math math r n cos n theta , math math n n 1 r n 2 cos n theta , math math n n 1 r n 2 sin n theta , math math n n 1 r n 2 cos n theta , math math r n 2 sin n theta , math math n 1 n 2 r n sin n theta , math math n n 1 r n cos n theta , math math n 1 n 2 r n sin n theta , math math r n 2 sin n theta , math math n 2 n 1 r n sin n theta , math math n n 1 r n cos n theta , math math ... n n 1 r n 2 cos n theta , math math n n 1 r n 2 sin n theta , math math r n sin n theta , math math ... more details
of math R H R S cos alpha math . Figure 1 illustrates the shooting scenario. The rule holds ... range math R H R S cos alpha math Use the bullet drop table to determine the bullet drop over that equivalent ... s rule to determine the equivalent horizontal range. math R H 300 mbox meters cos 20 circ 282 mbox ... in a vacuum. math x t v bullet cos delta theta t , math Equation 1 math y t v bullet sin delta theta ... cos delta theta math Equation 3 Equation 3 can be substituted in Equation 2. The resulting equation ... cos delta theta math math x frac v bullet 2 sin delta theta cos delta theta g , math Equation 4 where ... x R H math to obtain Equation 5. math R H frac v bullet 2 2 , sin delta theta , cos delta theta g ... Zero R H cos alpha math . Equation 8 demonstrates the correctness of this assertion. math R S R Zero sec alpha left R H cos alpha right sec alpha R H math Equation 8 This completes the demonstration .... math R S frac v Bullet 2 g , 2 sin theta cos theta left 1 frac cos theta sin theta frac sin alpha cos alpha right sec alpha , math Multiply the expression in the parentheses by the front trigonometric term. math R S frac v Bullet 2 g , , 2 left sin theta cos theta frac cos theta 2 sin alpha cos alpha right sec alpha , math Extract the factor math cos theta cos alpha math from the expression in parentheses. math R S frac v Bullet 2 g , 2 frac cos theta cos alpha left sin theta cos alpha sin alpha cos theta right sec alpha , math The expression inside the parentheses is in the form of a sine difference formula. Also, multiply the resulting expression by the factor math cos theta alpha cos theta alpha math . math R S frac v Bullet 2 g , left 2 sin theta alpha cos theta alpha right frac cos theta cos alpha cos theta alpha sec alpha , math Factor the expression math sin 2 theta alpha math from the expression inside the parentheses. In addition, add and subtract the expression math cos alpha cos theta alpha math inside the parentheses. math R S frac v Bullet 2 g , sin 2 left theta alpha ... more details
In mathematics and signal processing , the advanced Z transform is an extension of the Z transform , to incorporate ideal delays that are not multiples of the sampling rate sampling time . It takes the form math F z, m sum k 0 infty f k T m z k math where T is the sampling period m the delay parameter is a fraction of the sampling period math 0, T . math It is also known as the modified Z transform . The advanced Z transform is widely applied, for example to accurately model processing delays in digital control . Properties If the delay parameter, m , is considered fixed then all the properties of the Z transform hold for the advanced Z transform. Linearity math mathcal Z left sum k 1 n c k f k t right sum k 1 n c k F z, m . math Time shift math mathcal Z left u t n T f t n T right z n F z, m . math Damping math mathcal Z left f t e a , t right e a , m F e a , T z, m . math Time multiplication math mathcal Z left t y f t right left T z frac d dz m right y F z, m . math Final value theorem math lim k infty f k T m lim z 1 1 z 1 F z, m . math Example Consider the following example where math f t cos omega t math math begin align F z, m & mathcal Z left cos left omega left k T m right right right & mathcal Z left cos omega k T cos omega m sin omega k T sin omega m right & cos omega m mathcal Z left cos omega k T right sin omega m mathcal Z left sin omega k T right & cos omega m frac z left z cos omega T right z 2 2z cos omega T 1 sin omega m frac z sin omega T z 2 2z cos omega T 1 & frac z 2 cos omega m z cos omega T m z 2 2z cos omega T 1 end align math . If math m 0 math then math F z, m math reduces to the Z transform math F z, 0 frac z 2 z cos omega T z 2 2z cos omega T 1 math which is clearly just the Z transform of math f t . math See also Z transform Bibliography Eliahu Ibraham Jury , Theory and Application of the Z Transform Method , Krieger Pub Co, 1973. ISBN 0 88275 122 0. DSP Category Transforms pl Zmodyfikowana transformata Z ru Z ... more details
Morrie s law is a name that occasionally is used for the trigonometric identity math cos 20 circ cdot cos 40 circ cdot cos 80 circ frac 1 8 . math It is a special case of the more general identity math 2 n cdot prod k 0 n 1 cos 2 k alpha frac sin 2 n alpha sin alpha math with n 3 and 20 . The name is due to the physicist Richard Feynman , who used to refer to the identity under that name. Feynman picked that name because he learned it during his childhood from a boy with the name Morrie Jacobs and afterwards remembered it for all of his life. ref W.A. Beyer, J.D. Louck, and Doron Zeilberger D. Zeilberger , A Generalization of a Curiosity that Feynman Remembered All His Life , Math. Mag. 69, 43 44, 1996. ref A similar identity for the sine function also holds math sin 20 circ cdot sin 40 circ cdot sin 80 circ frac sqrt 3 8 . math Moreover, dividing the second identity by the first, the following identity is evident math tan 20 circ cdot tan 40 circ cdot tan 80 circ sqrt 3 tan 60 circ . , math Proof Recall the double angle formula for the sine function math sin 2 alpha 2 sin alpha cos alpha . , math Solve for math cos alpha math math cos alpha frac sin 2 alpha 2 sin alpha . math It follows that math begin align cos 2 alpha & frac sin 4 alpha 2 sin 2 alpha 6pt cos 4 alpha & frac sin 8 alpha 2 sin 4 alpha & , , , vdots cos 2 n 1 alpha & frac sin 2 n alpha 2 sin 2 n 1 alpha . end align math Multiplying all of these expressions together yields math cos alpha cos 2 alpha cos 4 alpha cdots cos 2 n 1 alpha frac sin 2 alpha 2 sin alpha cdot frac sin 4 alpha 2 sin 2 alpha cdot frac sin 8 alpha 2 sin 4 alpha cdots frac sin 2 n alpha 2 sin 2 n 1 alpha . math The intermediate numerators and denominators cancel leaving only the first denominator, a power of 2 and the final numerator. Note that there are n terms in both sides of the expression. Thus, math prod k 0 n 1 cos 2 k alpha frac sin 2 n alpha 2 n sin alpha , math which is equivalent to the generalization of Morrie s law. References ... more details
an axis by the following expression math mathbf q 0 cos alpha 2 math math mathbf q 1 sin alpha 2 cos beta x math math mathbf q 2 sin alpha 2 cos beta y math math mathbf q 3 sin alpha 2 cos beta z math where is a simple rotation angle the value in radians of the angle of rotation and cos sub x sub , cos sub y sub and cos sub z sub are the Direction cosine direction cosines locating the axis ..., , , with x y z convention, is given by math begin bmatrix cos theta cos psi & cos phi sin psi sin phi sin theta cos psi & sin phi sin psi cos phi sin theta cos psi cos theta sin psi & cos phi cos psi sin phi sin theta sin psi & sin phi cos psi cos phi sin theta sin psi sin theta & sin phi cos theta & cos phi cos theta end bmatrix math Conversion By combining the quaternion representations of the Euler rotations we get math mathbf q R z psi R y theta R x phi cos psi 2 mathbf k sin psi 2 cos theta 2 mathbf j sin theta 2 cos phi 2 mathbf i sin phi 2 math math mathbf q begin bmatrix cos phi 2 cos theta 2 cos psi 2 sin phi 2 sin theta 2 sin psi 2 sin phi 2 cos theta 2 cos psi 2 cos phi 2 sin theta 2 sin psi 2 cos phi 2 sin theta 2 cos psi 2 sin phi 2 cos theta 2 sin psi 2 cos phi 2 cos theta 2 sin psi 2 sin phi 2 sin theta 2 cos psi 2 end bmatrix math For Euler angles we get math begin bmatrix ... more details
Refimprove date September 2011 lead missing date June 2011 Class of service CoS main IEEE 802.1p As related to network technology, CoS is a 3 bit field that is present in an Ethernet frame header when 802.1Q VLAN tagging is present. The field specifies a priority value between 0 and 7, more commonly known as CS0 through CS7, that can be used by quality of service QoS disciplines to differentiate and shape police network traffic. CoS operates only on 802.1Q VLAN Ethernet at the data link layer layer 2 , while other QoS mechanisms such as DiffServ , also known as DSCP operate at the IP network layer layer 3 or use a local QoS tagging system that does not modify the actual packet, such as Cisco s QoS Group . Network devices i.e. routers, network switch switches , etc. can be configured to use existing CoS values on incoming packets from other devices trust mode , or can rewrite the CoS value to something completely different. Most Internet Service Providers do not trust incoming QoS markings from their customers, so CoS is generally limited to use within an organization s intranet. Classification of service The term can be used generically to refer to the Traffic classification classification of network traffic within network equipment based on packet inspection. Cisco implements such classification through either access lists or Network Based Application Recognition Network Based ... Cisco NBAR ref Class of service COS As related to legacy telephone systems, COS is often ... . The Class of Service acronym is normally written as COS vs. CoS as is often used in data networking ... calls outside the office. Permissions for a group of extensions can be changed by modifying a COS variable applied to the entire group. COS is also used on trunks to define if they are full duplex ... wwwcsif.cs.ucdavis.edu kramer papers cos jon.pdf Supporting differentiated classes of service in Ethernet ... Category Telephone exchanges de Class of Service ko CoS nl Class of service pl Class of service ... more details
to Cartesian coordinate transformation math begin align x & r sin theta cos varphi y & r sin theta sin varphi z & r cos theta end align math Spherical harmonics with l 0 math Y 0 0 theta, varphi 1 ... over 2 sqrt 3 over pi cdot cos theta quad quad 1 over 2 sqrt 3 over pi cdot z over r Y 1 1 theta, varphi ... over 2 pi cdot e i varphi cdot sin theta cdot cos theta quad 1 over 2 sqrt 15 over 2 pi cdot x iy z over r 2 math math Y 2 0 theta, varphi 1 over 4 sqrt 5 over pi cdot 3 cos 2 theta 1 quad 1 over 4 ... e i varphi cdot sin theta cdot cos theta quad 1 over 2 sqrt 15 over 2 pi cdot x iy z over r 2 math ... cdot cos theta quad 1 over 4 sqrt 105 over 2 pi cdot x iy 2 z over r 3 math math Y 3 1 theta, varphi 1 over 8 sqrt 21 over pi cdot e i varphi cdot sin theta cdot 5 cos 2 theta 1 quad 1 over 8 sqrt ... 5 cos 3 theta 3 cos theta quad 1 over 4 sqrt 7 over pi cdot z 2z 2 3x 2 3y 2 over r 3 math math Y 3 1 theta, varphi 1 over 8 sqrt 21 over pi cdot e i varphi cdot sin theta cdot 5 cos 2 theta 1 quad ... 105 over 2 pi cdot e 2i varphi cdot sin 2 theta cdot cos theta quad 1 over 4 sqrt 105 over 2 pi cdot ... 3 over 8 sqrt 35 over pi cdot e 3i varphi cdot sin 3 theta cdot cos theta frac 3 8 sqrt frac 35 ... cdot sin 2 theta cdot 7 cos 2 theta 1 frac 3 8 sqrt frac 5 2 pi cdot frac x i y 2 cdot 7 z 2 r 2 r 4 math math Y 4 1 theta, varphi 3 over 8 sqrt 5 over pi cdot e i varphi cdot sin theta cdot 7 cos 3 theta 3 cos theta frac 3 8 sqrt frac 5 pi cdot frac x i y cdot z cdot 7 z 2 3 r 2 r 4 math math Y 4 0 theta, varphi 3 over 16 sqrt 1 over pi cdot 35 cos 4 theta 30 cos 2 theta 3 frac 3 16 sqrt frac 1 ... e i varphi cdot sin theta cdot 7 cos 3 theta 3 cos theta frac 3 8 sqrt frac 5 pi cdot frac x i y cdot ... sin 2 theta cdot 7 cos 2 theta 1 frac 3 8 sqrt frac 5 2 pi cdot frac x i y 2 cdot 7 z 2 r 2 r 4 math math Y 4 3 theta, varphi 3 over 8 sqrt 35 over pi cdot e 3i varphi cdot sin 3 theta cdot cos theta ... cdot cos theta math math Y 5 3 theta, varphi 1 over 32 sqrt 385 over pi cdot e 3i varphi cdot sin ... more details
Function Derivative math sin x math math cos x math math cos x math math sin x math math tan x math ... functions include sin x , cos x and tan x . For example, in differentiating f x sin x , one is calculating ... . It turns out that once one knows the deriatives of sin x and cos x , one can easily compute the derivatives ... of sin x and cos x are given in the proofs section the results are quoted in order ... functions and their inverses math left sin x right cos x math math left cos x right sin x math math left tan x right left frac sin x cos x right frac cos 2 x sin 2 x cos 2 x frac 1 cos 2 x sec 2 x math math left cot x right left frac cos x sin x right frac sin 2 x cos 2 x sin 2 x 1 cot 2 x csc 2 x math math left sec x right left frac 1 cos x right frac sin x cos 2 x frac 1 cos x . frac sin x cos x sec x tan x math math left csc x right left frac 1 sin x right frac cos x sin 2 x frac 1 sin x . frac cos x sin x csc x cot x math math left arcsin x right frac 1 sqrt 1 x 2 math math left arccos x ... 1 tan &theta sin &theta cos &theta . If this is true then multiplication by two gives nowrap ... 1 sin theta frac 1 theta frac cos theta sin theta , . math Since &theta is small, and so less than ... cos theta , . math This tells us that for very small &theta , sin &theta &theta is less than 1, but is bigger than cos &theta . However, as &theta becomes smaller, cos &theta becomes bigger and gets ... than 1 and more than cos &theta but as &theta becomes smaller, cos &theta gets closer to 1. So, sin &theta &theta is sandwiched, or squeezed, between 1 and cos &theta as &theta becomes smaller and smaller. Obviously, the number 1 is fixed, and so as &theta becomes smaller and smaller, cos &theta ... theorem , also known as the squeeze theorem . Limit of cos &theta 1 &theta as &theta 0 The last section enables us to calculate this new limit easily. We find that math lim theta to 0 left frac cos theta 1 theta right lim theta to 0 left left frac cos theta 1 theta right left frac cos theta 1 cos ... more details
is any trigonometric function, and math cos x math is its derivative, math int a cos nx dx frac a n ... of integration . Integrals involving only sine math int sin ax dx frac 1 a cos ax C , math br math int sin 2 ax dx frac x 2 frac 1 4a sin 2ax C frac x 2 frac 1 2a sin ax cos ax C math br math int x sin 2 ax dx frac x 2 4 frac x 4a sin 2ax frac 1 8a 2 cos 2ax C math br math int x 2 sin 2 ax dx frac x 3 6 left frac x 2 4a frac 1 8a 3 right sin 2ax frac x 4a 2 cos 2ax C math br math int sin b 1x sin ... , math br math int sin n ax dx frac sin n 1 ax cos ax na frac n 1 n int sin n 2 ax dx qquad mbox for n ... frac dx sin n ax frac cos ax a 1 n sin n 1 ax frac n 2 n 1 int frac dx sin n 2 ax qquad mbox for n 1 mbox , math br math int x sin ax dx frac sin ax a 2 frac x cos ax a C , math br math int x n sin ax dx frac x n a cos ax frac n a int x n 1 cos ax dx sum k 0 2k leq n 1 k 1 frac x n 2k a 1 2k frac n n 2k cos ax sum k 0 2k 1 leq n 1 k frac x n 1 2k a 2 2k frac n n 2k 1 sin ax qquad mbox for n 0 mbox ... 2n 1 C , math br math int frac sin ax x n dx frac sin ax n 1 x n 1 frac a n 1 int frac cos ax x ... br math int frac x dx 1 sin ax frac x a tan left frac ax 2 frac pi 4 right frac 2 a 2 ln left cos left ... only cosine math int cos ax dx frac 1 a sin ax C , math math int cos 2 ax dx frac x 2 frac 1 4a sin 2ax C frac x 2 frac 1 2a sin ax cos ax C math math int cos n ax dx frac cos n 1 ax sin ax na frac n 1 n int cos n 2 ax dx qquad mbox for n 0 mbox , math math int x cos ax dx frac cos ax a 2 frac x sin ax a C , math math int x 2 cos 2 ax dx frac x 3 6 left frac x 2 4a frac 1 8a 3 right sin 2ax frac x 4a 2 cos 2ax C math math int x n cos ax dx frac x n sin ax a frac n a int x n 1 sin ax dx , sum k 0 2k 1 leq n 1 k frac x n 2k 1 a 2 2k frac n n 2k 1 cos ax sum k 0 2k leq n 1 k frac x n 2k a 1 2k frac n n 2k sin ax math math int frac cos ax x dx ln ax sum k 1 infty 1 k frac ax 2k 2k cdot 2k C , math math int frac cos ax x n dx frac cos ax n 1 x n 1 frac a n 1 int frac sin ax x n 1 dx qquad mbox ... more details
n it holds that math cos x i sin x n cos nx i sin nx . , math The formula is important because it connects ... . The expression cos x i sin x is sometimes abbreviated to cis x . By expanding the left ... to derive useful expressions for cos nx and sin nx in terms of cos x and sin x . Furthermore ... in complex analysis Euler s formula math e ix cos x i sin x , math and the exponentiation exponential ... cos nx i sin nx . , math Failure for non integer powers De Moivre s formula does not, in general, hold ... there. Consider S n math cos x i sin x n cos nx i sin nx , n in mathbb Z . math For n 0 ... for some natural k . That is, we assume math left cos x i sin x right k cos left kx right i sin left kx right . , math Now, considering S k 1 math begin alignat 2 left cos x i sin x right k 1 & left cos x i sin x right k left cos x i sin x right & left cos left kx right i sin left kx right right left cos x i sin x right && qquad text by the induction hypothesis & cos left kx right cos x sin left kx right sin x i left cos left kx right sin x sin left kx right cos x right & cos left left k 1 right ..., we consider an exponent of n for natural n . math begin align left cos x i sin x right n & left left cos x i sin x right n right 1 & left cos nx i sin nx right 1 & cos nx i sin nx . qquad end align math The equation is a result of the identity math z 1 frac bar z z 2 math , for z cos nx i sin nx ... math sin nx sum k 0 n binom n k cos kx , sin n k x , sin left frac 1 2 n k pi right math math cos nx sum k 0 n binom n k cos kx , sin n k x , cos left frac 1 2 n k pi right . math In each of these two ... alignat 2 cos 2x & cos x 2 cos x 2 1 && 2 cos x 2 1 sin 2x & 2 sin x cos x cos 3x & cos x 3 3 cos x cos x 2 1 && 4 cos x 3 3 cos x sin 3x & 3 cos x 2 sin x sin x 3 && 3 sin x 4 sin x 3. end alignat math The right hand side of the formula for cos nx is in fact the value T sub n sub cos x of the Chebyshev ... general setting than stated above if z and w are complex numbers, then math left cos z i sin ... more details
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