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 π θ << or 0 90 °< < ° . opposite sin hypotenuse = hypotenuse csc opposite = adjacent cos hypotenuse = hypotenuse sec adjacent = opposite tan adjacent = adjacent cot opposite = Unit circle definition For this definition is any angle. sin 1 y y == 1 csc y = cos 1 x x 1 sec x = tan y x = cot x y = Facts and Properties Domain The domain is all the values of that can be plugged into the function. sin , can be any angle cos , can be any angle tan , 1 ,0 , 1 , 2 , 2 nn θπ ⎛⎞ ≠+ = ± ± ⎜⎟ ⎝⎠ csc , , 1 , 2 , ≠= ± ± sec , 1 , 1 , 2 , 2 = ± ± cot , , 1 , 2 , ± ± Range The range is all possible values to get out of the function. 1s i n 1 −≤ csc 1 and csc 1 θθ ≥≤ 1 cos 1 sec 1 andsec 1 tan −∞ ≤ ≤ ∞ cot −∞ ≤ ≤ ∞ Period The period of a function is the number, T , such that ( )( ) fT f += . So, if ω is a fixed number and is any angle we have the following periods. ( ) sin ωθ 2 T = ( ) cos 2 T = ( ) tan T = ( ) csc 2 T = ( ) sec 2 T = ( ) cot T = adjacent opposite hypotenuse x y ( ) , xy x y 1
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© 2005 Paul Dawkins Formulas and Identities Tangent and Cotangent Identities sin cos tan cot cos sin θθ == Reciprocal Identities 11 csc sin sin
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Trig Cheat Sheet - Trig Cheat Sheet Definition of the Trig...

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