Trigonometric Functions and the Unit Circle

This video tutorial explains how to find values of trigonometric functions using the unit circle. It covers the basics of sine, cosine, and tangent, and demonstrates how to calculate these functions for specific angles such as 60 degrees, 5 pi over 3, 225 degrees, 150 degrees, and 2 pi over 3. The unit circle is used to provide exact values for these trigonometric functions, emphasizing accuracy over decimal approximations.

What is the primary purpose of the unit circle in trigonometry?

• To measure angles in degrees

• To solve algebraic equations

• To find exact values of trigonometric functions

• To convert radians to degrees

Which coordinate on the unit circle represents the sine of an angle?

• X-coordinate

• Y-coordinate

• Origin

• Z-coordinate

How is the cosine of an angle determined using the unit circle?

• By the tangent line

• By the X-coordinate

• By the radius

• By the Y-coordinate

What is the sine of 60° according to the unit circle?

• √3/2

• √2/2

• 1/2

• 1

What is the cosine of 5π/3?

• 1/2

• √3/2

• 1

• 0

How do you calculate the tangent of an angle using the unit circle?

• Y/X

• X/Y

• X*Y

• X+Y

What is the tangent of 225°?

• 1

• -1

• 0

• Undefined

What is the cosine of 150°?

• √3/2

• -√3/2

• -1/2

• 1/2

What is the tangent of 2π/3?

• -1

• √3

• -√3

• 1

Why is the unit circle useful for trigonometric calculations?

• It measures angles in radians

• It provides approximate values

• It simplifies complex numbers

• It gives exact trigonometric values