Notes 6-8: Principal Values and Inverses

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Presentation transcript:

Notes 6-8: Principal Values and Inverses domain range graph y = Sinx y = Cosx y = Tanx Uppercase notation indicates principal values (restricted domain and range) ↑

angle measure θ /6 /4 /3 sinθ cosθ tanθ 1 30° 45° 60° side ratio

Inverse Notation:

The principal values of the trig functions allow us to find unique solutions when solving for an inverse. Examples: a) sin /4 = b) tan /3 = c) Arccos = d) Arcsin ½ =

e) given: y = Arctan(2x) Find the inverse algebraically. x = Arctan(2y) Swap domain and range, then put back into y-form

f) given: y = 2cos(x + /4) Find the inverse algebraically f) given: y = 2cos(x + /4) Find the inverse algebraically. x = 2cos(y + /4) Swap domain and range, then put back into y-form 7