Unit Circle Mastery

Unit Circle Mastery

Read each question carefully and provide your answers using your knowledge of the unit circle. Show all your work where applicable.

1. What is the radius of the unit circle and why is it significant?

2. Explain how the coordinates (x, y) of a point on the unit circle relate to the cosine and sine of the angle formed with the positive x-axis.

3. The cosine of 90 degrees (or π/2 radians) is  .

4. The sine of 180 degrees (or π radians) is  .

5. The coordinates for the angle 3π/2 radians on the unit circle are  .

6. Which of the following angles has a sine value of 1/2?

7. For an angle θ in the unit circle, if cos(θ) = -√3/2 and sin(θ) = 1/2, in which quadrant does θ lie?

8. The tangent of an angle θ on the unit circle can be found by dividing the x-coordinate by the y-coordinate.

9. The terminal side of an angle of -45 degrees is in the same position as an angle of 315 degrees on the unit circle.

10. If a point on the unit circle has coordinates (-1/2, -√3/2), what are the possible angles (in radians) that correspond to this point?