csc q ³ 1 and csc q £ -1 -1 £ sin q £ 1 sec q ³ 1 and sec q £ -1 -1 £ cos q £ 1 -¥ < tan q < ¥ -¥ < cot q < ¥ csc (wq ) ® T sec ( wq ) ® T cot ( wq ) ® T csc q, sec q, cot q, Tangent and Cotangent Identities sin q cos q tan q = cot q = cos q sin q Reciprocal Identities 1 1 csc q = sin q = sin q csc q 1 1 secq = cos q = cos q sec q 1 1 cot q = tan q = tan q cot q Pythagorean Identities sin 2 q + cos 2 q = 1 © 2005 Paul Dawkins 1 + cot 2 q = csc 2 q Even/Odd Formulas sin ( -q ) = - sin q csc ( -q ) = - csc q cos ( -q ) = cos q sec ( -q ) = sec q tan ( -q ) = - tan q cot ( -q ) = - cot q Periodic Formulas If n is an integer. 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. Trigonometry is the study of triangles, which contain angles, of course.

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°.

Trig triangle cheat sheet