Trigonometric Formulas
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Trigonometric Formulas Half Angle Identities s sin( =2) = s cos( =2) = 1 cos( ) 2 1 + cos( ) 2 v u u1 t cos( ) 1 + cos( ) tan( =2) = Power Reducing Identities 1 cos(2u) 2 1 + cos(2u) cos2 (u) = 2 1 cos(2u) tan2 (u) = 1 + cos(2u) sin2 (u) = Product to Sum Formulas 1 [sin(u + v) + sin(u v)] 2 1 cos u sin v = [sin(u + v) sin(u v)] 2 1 cos u cos v = [cos(u + v) + cos(u v)] 2 1 sin u sin v = [cos(u + v) cos(u v)] 2 sin u cos v = Sum to Product Formulas Angle 0 0 cos 0 1 tan 0 sin 30 6 1 p2 3 2 p 3 3 45 p4 2 p2 2 2 1 60 p3 3 2 1 2 p 3 sin + sin sin sin cos + cos cos cos 90 2 1 0 +1 + ) cos( )] 2 2 + = 2[cos( ) sin( )] 2 2 + = 2[cos( ) cos( )] 2 2 + = 2[sin( ) sin( )] 2 2 = 2[sin( 120 135 150 2 p3 3 2 1 2 3 p4 2 2 p 2 2 5 6 1 2 p p 3 1 2p 180 0 1 3 3 0 3 1 210 225 240 270 300 315 7 6 1 2 p 3 2 p 5 4 p 4 3 p 3 2 5 3 p 7 4 p 3 3 2 p 2 1 2 2 3 2 1 2 p 3 1 0 1 2 1 2 3 p 3 2 p2 2 2 1 330 360 11 2 6 1 p2 3 2p 3 3 0 1 0 Quotient identities sin( cos( cos( cot( ) = sin( tan( ) = ) ) ) ) Reciprocal identities 1 cos( ) 1 csc( ) = sin( ) 1 cot( ) = tan( ) sec( ) = Pythagorean identities sin2 ( ) + cos2 ( ) = 1 1 + tan2 ( ) = sec2 ( ) 1 + cot2 ( ) = csc2 ( ) Sum and Di erence formulas sin(u + v) sin(u v) cos(u + v) cos(u v) = = = = sin(u) cos(v) + cos(u) sin(v) sin(u) cos(v) cos(u) sin(v) cos(u) cos(v) sin(u) sin(v) cos(u) cos(v) sin(u) sin(v) tan(u) + tan(v) tan(u + v) = 1 tan(u) tan(v) tan(u) tan(v) tan(u v) = 1 + tan(u) tan(v) Double angle formulas sin(2 ) = cos(2 ) = = = 2 sin( ) cos( ) cos2 ( ) sin2 ( ) 2 cos2 ( ) 1 1 2 sin2 ( ) 2 tan( ) tan(2 ) = 1 tan2 ( ) 2
