Understanding Trigonometric Functions Using the Unit Circle

This video tutorial explains how to determine exact trigonometric function values when an angle is given in radians using the unit circle. It covers sketching the angle 7PI/2 radians in standard position and calculating the cosine, sine, and tangent values. The tutorial also discusses reciprocal trigonometric functions, including cotangent, secant, and cosecant, and their values for the given angle.

What is the relationship between the terminal side of an angle and the unit circle in determining trigonometric values?

• The terminal side intersects the unit circle to give cosine and sine values.

• The terminal side only affects the tangent value.

• The terminal side is irrelevant to trigonometric values.

• The terminal side determines the radius of the circle.

How many radians are in one complete counter-clockwise revolution?

• π radians

• 2π radians

• 3π radians

• 4π radians

What are the coordinates of the terminal side of the angle 7π/2 on the unit circle?

• (1, 0)

• (0, 1)

• (0, -1)

• (-1, 0)

What is the cosine value for the angle 7π/2?

• 1

• 0

• Undefined

• -1

What is the sine value for the angle 7π/2?

• Undefined

• -1

• 0

• 1

Why is the tangent of 7π/2 undefined?

• Because the angle is not on the unit circle.

• Because the cosine is zero.

• Because the sine is zero.

• Because both sine and cosine are zero.

What is the value of cotangent for the angle 7π/2?

• 0

• Undefined

• 1

• -1

What is the secant of 7π/2?

• 1

• -1

• 0

• Undefined

What is the cosecant of 7π/2?

• Undefined

• -1

• 0

• 1

Which trigonometric function is the reciprocal of sine?

• Tangent

• Cosine

• Secant

• Cosecant