1. 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) ↑

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

3. Inverse Notation:

5. 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 =

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

7. 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