2p w 2p = w p = w 2p = w 2p = w p = w sin ( wq ) ® T= 1ö æ q ¹ ç n + ÷ p, n = 0, ± 1, ± 2, K 2ø è q ¹ n p, n = 0, ± 1, ± 2, K cos (wq ) ® T tan (wq ) ® T Range The range is all possible values to get out of the function. So, if w is a fixed number and q is any angle we have the following periods. sin q, cos q, tan q, q can be any angle q can be any angle 1ö æ q ¹ ç n + ÷ p, n = 0, ± 1, ± 2, K 2ø è q ¹ n p, n = 0, ± 1, ± 2, K Period The period of a function is the number, T, such that f (q + T ) = f (q ). y ( x, y ) hypotenuse y opposite 1 q x x q tan 2 q + 1 = sec 2 q adjacent opposite hypotenuse adjacent cos q = hypotenuse opposite tan q = adjacent sin q = hypotenuse opposite hypotenuse sec q = adjacent adjacent cot q = opposite csc q = y sin q = y 1 x cos q = x 1 y tan q = x 1 csc q = y 1 sec q = x x cot q = y Facts and Properties Domain The domain is all the values of q that can be plugged into the function. 2 Unit circle definition For this definition q is any angle. Formulas and Identities Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that p 0 < q < or 0° < q < 90°.
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