# Trig_Cheat_Sheet - Trig Cheat Sheet Definition of the Trig...

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© 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 ° < < ° . 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. 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. 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 ± ² + = ³ ´ L l K csc q , , 0, 1, 2, n n q p = K sec q , 1 , 0, 1, 2, 2 n n q p ± ² + = ³ ´ 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. 1 sin 1 q - £ £ csc 1 andcsc 1 q q £ - 1 cos 1 q - £ £ sec 1 andsec 1 q q £ - tan q -¥ < < ¥ cot q -¥ < < ¥ Period The period of a function is the number, T , such that ( ) ( ) f T f q q + = . So, if w is a fixed number and q is any angle we have the following periods.