Grade 12 Unit Circle Mastery Worksheet

Grade 12 Unit Circle Mastery Worksheet

Read each question carefully and provide the best answer. Show all your work for full credit. You may refer to a unit circle diagram if needed.

1. What is the definition of the unit circle in trigonometry?

2. Explain the relationship between the coordinates (x, y) on the unit circle and the trigonometric functions sine and cosine for an angle θ.

Use the unit circle diagram below to answer the following questions.

3. What are the coordinates on the unit circle for an angle of 270°?

4. If the terminal side of an angle θ in standard position passes through the point (-√3/2, 1/2) on the unit circle, what is the value of sin(θ)?

5. The radian measure of an angle is the ratio of the arc length to the  .

6. An angle of 3π/2 radians is equivalent to   degrees.

7. The tangent of an angle θ on the unit circle is defined as the ratio of   to  .

8. Find the exact values of sin(θ), cos(θ), and tan(θ) for an angle θ = 5π/6 radians. Show your work.

9. If cos(θ) = -1/2 and θ is in Quadrant III, find the exact value of sin(θ).

10. The range of the sine function is [-1, 1].

11. The terminal side of 450° lies on the positive y-axis.