List of trigonometric identities

Some ex amples of this are s hown by s hifting func

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Unformatted text preview: ts more s imply . Some ex amples of this are s hown by s hifting func tions round by π/2, π and 2π radians . Bec aus e the periods of thes e func tions are either π or 2π, there are c as es where the new func tion is ex ac tly the s ame as the old func tion without the s hift. Shift by π/2 Shift by π Pe riod for ta n a nd cot[6] en.wikipedia.or g /wiki/List_of_tr ig onometr ic_identities Shift by 2π Pe riod for sin, cos, csc a nd se c[7] 2/12 12/7/13 List of tr ig onometr ic identities - Wikipedia, the fr ee encyclopedia Angle sum and dif f erence identities [edit] See als o: #Produc t-to-s um and s um-to-produc t identities Thes e are als o k nown as the addition and s ub trac tion theorems or formulae. They were originally es tablis hed by the 10th c entury Pers ian mathematic ian Abū al-W afā' Būz jānī. One method of proving thes e identities is to apply Euler's formula. The us e of the s y mbols and is des c ribed in the artic le plus -minus s ign. For the angle addition diagram for the s ine and c os ine, the line in bold with the 1 on it is of length 1. It is the hy potenus e of a right angle triangle with angle β whic h gives the s in β and c os β. The c os β line is the hy potenus e of a right angle triangle with angle α s o it has s ides s in α and c os α both multiplied by c os β. This is the s ame for the s in β line. The original line is als o the hy potenus e of a right angle triangle with angle α + β, the oppos ite s ide is the s in(α + β) line up from the origin and the adjac ent s ide is the c os (α + β) s egment going horiz ontally from the top left. Overall the diagram c an be us ed to s how the s ine and c os ine of s um identities bec aus e the oppos ite s ides of the rec tangle are equal. S i ne [8][9] Cosine [9][10] [9][11] Ta nge nt [12] Arcsine [13] Arccosine [14] Arcta nge nt Matrix form Illus tr ation of angle addition f or mulae f or the s ine and c os ine. Emphas iz ed s egment is of unit length. [edit] See als o: matrix multiplic ation The s um and differenc e formulae for s ine and c os ine c an be written in matrix form as : Illus tr ation of the angle addition f or mula f or the tangent. Emphas iz ed s egments ar e of unit length. This s hows that thes e matric es form a repres entation of the rotation group in the plane (tec hnic ally , the s pec ial orthogonal group SO(2)), s inc e the c ompos ition law is fulfilled: s ubs equent multiplic ations of a vec tor with thes e two matric es y ields the s ame re...
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This document was uploaded on 02/04/2014.

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