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Symbolab Trigonometry Cheat Sheet Basic Identities: (tan )=sin(𝑥) cos(𝑥) (tan )= 1 cot(𝑥) (cot )= 1 tan(𝑥)) cot( )=cos(𝑥) sin(𝑥) sec( )= 1 cos(𝑥) csc( = 1 sin(𝑥) Pythagorean Identities (cos 2 )+sin( )=1 2sec( )−tan2( )=1 2csc( )−cot2( )=1 Double Angle Identities
Function Ranges. y = \sin (x) -1\le y\le 1. y = \cos (x) -1\le y\le 1. y = \tan (x) -\infty < y <\infty. y = \cot (x) -\infty < y <\infty. y = \csc (x) -\infty < y\le -1\:\bigcup \:1\le y < \infty. y = \sec (y) -\infty < y\le -1\:\bigcup \:1\le y < \infty.
Facts and Properties. Domain. The domain is all the values of θ that can be plugged into the function. sinθ , θ can be any angle cosθ , θ can be any angle. 1 tanθ , ⎛ θ ≠ ⎜ n + ⎞ ⎟ π , n = 0, ± 1, ± 2, ... ⎝ 2 ⎠ cscθ , θ ≠ n π = ± ± , n 0, 1, 2, ... secθ θ ≠ ⎛ 1 ⎞ , ⎜ ⎝ n + ⎟ π , n = 0, ± 1, ± 2, ... 2 ⎠.
Facts and Properties. Domain. The domain is all the values of θ that can be plugged into the function. sinθ , cosθ , tanθ ,
Quotient Identities. sin. tan = cos cos. cot = sin.
Sum & Difference Identities: sin( + )=sin cos +cos sin sin ( − ) = sin cos − cos sin cos( + )=cos cos −sin sin
The period of a function is the number, T, such that f ( q + T ) = f ( q ) . So, if w is a fixed number and q is any angle we have the following periods. sin ( wq ) cos ( wq ) ( wq ) tan. csc ( wq ) sec ( wq ) cot ( wq ) 2 p.
