Exploring Unit Circle Trigonometric Values

The video tutorial explains how to connect the six trigonometric functions with the unit circle. It covers the basic definitions of sine, cosine, tangent, and their reciprocal functions: cosecant, secant, and cotangent. The tutorial provides examples of finding these functions' values using the unit circle, both in degrees and radians. It also demonstrates how to simplify fractions and handle radicals in the denominator. The video emphasizes the importance of understanding the unit circle and provides a cheat sheet for quick reference.

What is the radius of the unit circle used in trigonometry?

• 10

• 0.5

• 2

• 1

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

• None of the above

• y-coordinate

• x-coordinate

• z-coordinate

What is the reciprocal trigonometric function of sine?

• Cosecant

• Secant

• Cotangent

• Cosine

How do you find the cosine of an angle using the unit circle?

• None of the above

• Use the y-coordinate

• Multiply x and y coordinates

• Use the x-coordinate

What is the value of sine for 45 degrees in the unit circle?

• 1

• sqrt(2)/2

• 1/2

• sqrt(3)/2

What is the value of cosine at 2 pi over 3 radians?

• sqrt(3)/2

• -1/2

• -sqrt(3)/2

• 1/2

How is tangent of an angle calculated in the unit circle?

• y-coordinate over x-coordinate

• x-coordinate minus y-coordinate

• x-coordinate plus y-coordinate

• x-coordinate over y-coordinate

What happens to the secant of an angle when the cosine of that angle is zero?

• It is 0

• It is 1

• It is undefined

• It is -1

What is the simplified form of cotangent when the angle is 315 degrees?

• Undefined

• 1

• 0

• -1

What is the result of cosecant of five pi over 4?

• sqrt(2)

• -sqrt(2)

• -2/sqrt(2)

• 2/sqrt(2)