You are working with a triangular brace in shop class. The brace is a right triangle, and the length of one side of the bracket is

Can you find the angle between the legs of the brace?

By the time you finish reading this lesson, you'll be able to answer this question.

### Inverse of Sine, Cosine and Tangent

Inverse trig functions can be useful in a variety of math problems for finding angles that you need to know. In many cases, such as angles involving multiples of

Recall the unit circle and the critical values. With the inverse trigonometric functions, you can find the angle value (in either radians or degrees) when given the ratio and function. Make sure that you find all solutions within the given interval.

Let's take a look at a few example problems.

1. Find the exact value of the expression without a calculator, in

This is a value from the special right triangles and the unit circle.

Recall that

2. Find the exact value of the expression without a calculator, in

This is a value from the special right triangles and the unit circle.

3. Find the exact value of the expression without a calculator, in

This is a value from the special right triangles and the unit circle.

### Examples

#### Example 1

Earlier, you were asked to find the angle between the legs of the brace.

Using your knowledge of the values of trig functions for angles, you can work backward to find the angle that the brace makes:

#### Example 2

Find the exact value of the inverse function of

#### Example 3

Find the exact value of the inverse function of

#### Example 4

Find the exact value of the inverse function of

### Review

Find the exact value of each expression without a calculator, in

sin−1(2√2) cos−1(12) sin−1(1) cos−1(−3√2) tan−1(−3√3) tan−1(−1) sin−1(3√2) cos−1(2√2) csc−1(2√) sec−1(−2) cot−1(3√3) sec−1(23√2) csc−1(−23√2) cot−1(−3√) cot−1(−1)

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.2.