Trigonometric Functions and Angles

This video tutorial explains how to find the exact values of circular functions using the unit circle. It covers the definitions of sine, cosine, tangent, cotangent, secant, and cosecant, and provides examples for calculating these functions at specific angles, including quadrantal angles and angles with reference angles. The tutorial emphasizes the importance of understanding the unit circle and the coordinates of terminal points to determine the values of circular functions.

What is the primary tool used to find the exact values of circular functions?

• Graph paper

• Unit circle

• Calculator

• Protractor

Which angles are considered quadrantal angles?

• 45°, 135°, 225°, 315°

• 0°, 90°, 180°, 270°

• 30°, 60°, 120°, 150°

• 15°, 75°, 105°, 165°

What is the sine of an angle defined as on the unit circle?

• 1/x

• x/y

• y-coordinate

• x-coordinate

What is the cosine of an angle defined as on the unit circle?

• 1/y

• x/y

• y-coordinate

• x-coordinate

What is the tangent of an angle defined as on the unit circle?

• y/x

• x-coordinate

• 1/x

• y-coordinate

What is the cotangent of an angle defined as on the unit circle?

• 1/x

• y/x

• x/y

• 1/y

What is the secant of an angle defined as on the unit circle?

• 1/x

• y-coordinate

• 1/y

• x-coordinate

What is the cosecant of an angle defined as on the unit circle?

• 1/y

• x-coordinate

• y-coordinate

• 1/x

For the angle 3π/2, what is the value of sine?

• -1

• Undefined

• 1

• 0

For the angle 3π/2, what is the value of cosine?

• 0

• Undefined

• 1

• -1