1. Example 1: Finding Trigonometric Inverses
Warm Up
Convert each measure from degrees to radians.
1. 120° °
Find the exact value of each trigonometric function.
Learning Goals
Evaluate inverse trigonometric functions.
Use trigonometric equations & inverse trigonometric functions to solve problems.
The expression sin-1 is read as “the inverse sine.” In this notation,-1 indicates the inverse of the sine function, NOT the sine function to the ______ ____________.
Function
Inverse
Example 1: Finding Trigonometric Inverses
Find all possible _________________ values.
A. cos-1
B. tan-1 1
sin-1(-½).

2. Domain Restrictions for Sin, Cos, and Tan
Notice that more than one θ has the same output for any trig function.
EXAMPLE:
So, we have to restrict the domain for the function so we can find _________ angle instead of __________________ angles to correspond with the value.
Trigonometric functions with restricted domains are indicated __________ ___ _____________ _____________.
Domain Restrictions for Sin, Cos, and Tan
Sinθ
sinθ for
{θ| }
Cosθ
cosθ for
Tanθ
tanθ for
How many values does tan-1 1 have?
How many values does Tan-11 have?
How what sort of values do you plug in to Sin, Cos, and Tan?
What sort of values do you plug in to Sin-1, Cos-1, and Tan-1?

3. Example 2: Evaluating Inverse Trigonometric Functions
Symbol
Alt. Symbol
Domain
Range
Sin-1(r)
Cos-1(r)
Tan-1(r)
Example 2: Evaluating Inverse Trigonometric Functions
Evaluate each inverse trigonometric function. Give your answer in both radians and degrees.
A B.
C. D.
E. Sin F. Tan-1 (0)

4. Solve each equation to the nearest tenth. Use the given restrictions.
A. sin θ = 0.4, for – 90° ≤ θ ≤ 90°
B. sin θ = 0.4, for 90° ≤ θ ≤ 270°
C. tan θ = –2, for –90° < θ < 90°
D. tan θ = –2, for 90° < θ < 180°

5. Example 3: Solving Trigonometric Equations
Solve each equation to the nearest tenth. Use the given restrictions.
C. cos θ = 0.3, for 0° ≤ θ ≤ 180°
D. cos θ = 0.3, for 270° < θ < 360°
Example 4: Safety Application
A. A painter needs to lean a 30 ft ladder against a wall. Safety guidelines recommend that the distance between the base of the ladder and the wall should be ¼ of the length of the ladder. To the nearest degree, what acute angle should the ladder make with the ground?
B. A group of hikers wants to walk form a lake to an unusual rock formation. The formation is 1 mile east and 0.75 mile north of the lake. To the nearest degree, in what direction should the hikers head from the lake to reach the rock formation?