Understanding Inverse Trigonometric Functions

The video tutorial explains how to evaluate trigonometric expressions involving inverse functions. It covers the simplification of expressions like inverse cosine of cosine pi/3, inverse cosine of cosine 11/6 pi, inverse sine of sine 3/4 pi, and inverse sine of sine 3/2 pi. The tutorial emphasizes the importance of understanding angle intervals and the unit circle to correctly simplify these expressions.

What is the result of inverse cosine of cosine pi over three?

• Zero

• Pi over six

• Pi over three

• Pi

Why is it important to consider the interval when evaluating inverse trigonometric functions?

• To find the correct angle within the specified range

• To simplify calculations

• To ensure the angle is positive

• To avoid complex numbers

What is the simplified result of inverse cosine of cosine 11/6 pi?

• Pi over three

• Zero

• Pi over six

• Pi

What is the value of sine 3/4 pi?

• Square root of two divided by two

• One

• Zero

• Negative one

What is the result of inverse sine of sine 3/4 pi?

• Pi over four

• Pi over two

• Zero

• Pi

What is the y-coordinate of the terminal side for sine 3/2 pi?

• Zero

• One

• Negative one

• Square root of two divided by two

What is the result of inverse sine of sine 3/2 pi?

• Pi over two

• Pi

• Negative pi over two

• Zero

Why is the rotation clockwise for the angle in inverse sine of sine 3/2 pi?

• To find a positive angle

• To stay within the interval

• To simplify the expression

• To match the original angle

What is the interval for the inverse sine function?

• Zero to two pi

• Negative pi over two to pi over two

• Zero to pi

• Negative pi to pi

What is the importance of the unit circle in evaluating trigonometric expressions?

• It helps find the exact values of trigonometric functions

• It simplifies complex numbers

• It is used to calculate derivatives

• It provides a visual representation of angles