Download Trigonometry Formulas Cheat Sheet and more Cheat Sheet Trigonometry in PDF only on Docsity! TRIGONOMETRY FORMULAS 1)(sin)(cos 22 =+ xx )(sec)(tan1 22 xx =+ )(csc1)(cot 22 xx =+ cos( ) cos( )cos( ) sin( )sin( ) sin( ) sin( ) cos( ) cos( )sin( ) x y x y x y x y x y x y ± = ± = ± ∓ )tan()tan(1 )tan()tan( )tan( yx yx yx ∓ ± =± )(tan1 )tan(2 )2tan( )(sin21 1)(cos2 )(sin)(cos )2cos( )cos()sin(2)2sin( 2 2 2 22 x x x x x xx x xxx − = − − − = = 2 2 2 2 cos( ) sin( ) sin( ) sin( ) c a b ab C A B C a b c = + − = = )2cos(1 )2cos(1 )(tan 2 )2cos(1 )(cos 2 )2cos(1 )(sin 2 2 2 x x x x x x x + − = + = − = )cos(1 )cos(1 2 tan 2 )cos(1 2 sin 2 )cos(1 2 cos x xx xx xx + − ±= − ±= + ±= ( ) ( ) ( ) ( ) )]sin([sin)sin()cos( )]sin([sin)cos()sin( )]cos([cos)cos()cos( )]cos([cos)sin()sin( 2 1 2 1 2 1 2 1 yxyxyx yxyxyx yxyxyx yxyxyx −−+= −++= ++−= +−−= − + −=− − + =+ + − =− − + =+ 2 sin 2 sin2)cos()cos( 2 cos 2 cos2)cos()cos( 2 cos 2 sin2)sin()sin( 2 cos 2 sin2)sin()sin( yxyx yx yxyx yx yxyx yx yxyx yx For two vectors A and B, A·B = ||A||||B||cos(θ) Department of Mathematics & Statistics – Arizona State University 2 The well known results: soh, cah, toa soh: s stands for sine, o stands for opposite and h stands for hypotenuse, sin o x h = cah: c stands for cosine, a stands for adjacent h stands for hypotenuse, cos a x h = h o toa: t stands for tan, o stands for opposite and a stands for adjacent, tan o x a = a Where x is the angle between the hypotenuse and the adjacent. Other three trigonometric functions have the following relations: 1 csc sin h x x o = = , 1 sec cos h x x a = = and 1 cot tan a x x o = = Important values: 0 030 6 π = 045 4 π = 060 3 π = 090 2 π = sin 0 1 2 2 2 3 2 1 cos 1 3 2 2 2 1 2 0 tan 0 1 3 1 3 undefined csc undefined 2 2 2 3 1 sec 1 2 3 2 2 undefined cot undefined 3 1 1 3 0 sin( ) [?]sin , cos( ) [?]cos , tan( ) [?] tann x x n x x n x xπ π π± = ± = ± = , the sign ? is for plus or minus depending on the position of the terminal side. One may remember the four-quadrant rule: (All Students Take Calculus: A = all, S = sine, T = tan, C = cosine) sine all tan cosine
