![]() ![]() ( ) sin wq fi 2 T p w = ( ) cos wq fi 2 T p w = ( ) tan wq fi T p w = ( ) csc wq fi 2 T p w = ( ) sec wq fi 2 T p w = ( ) cot wq fi T p w = q adjacent opposite hypotenuse x y ( ), xy q x y 1ĭefinition of the Trig Functions Right triangle definition For this definition we assume that So, if w is a fixed number and q is any angle we have the following periods. 1 sin 1 q -£ £ csc 1 and csc 1 q q ‡ £- 1 cos 1 q -£ £ sec 1 and sec 1 q q ‡ £- tan q -¥ < <¥ cot q -¥ < <¥ Period The period of a function is the number, T, such that ( ) ( ) f T f q q + =. sin q, q can be any angle cos q, q can be any angle tan q, 1, 0, 1, 2, 2 n n q p „ + = – – L l K csc q, , 0, 1, 2, n n q p „ = – – K sec q, 1, 0, 1, 2, 2 n n q p „ + = – – L l K cot q, , 0, 1, 2, n n q p „ = – – K Range The range is all possible values to get out of the function. sin 1 y y q = 1 csc y q = cos 1 x x q = 1 sec x q = tan y x q = cot x y q = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. ![]() opposite sin hypotenuse q = hypotenuse csc opposite q = adjacent cos hypotenuse q = hypotenuse sec adjacent q = opposite tan adjacent q = adjacent cot opposite q = Unit circle definition For this definition q is any angle. © 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 p q < < or 0 90 q < <. ![]()
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