Developing the Unit Circle

Developing the Unit Circle, Part 1
Name ___________________________

Period ___________________________

1. Using the right triangle diagram, write an equation for x in
terms of θ.

2. Using the right triangle diagram, write an equation for y in
terms of θ.

Use this triangle for #1-2:

3. What is the value of a when the hypotenuse is 1 unit?

4. What is the value of b when the hypotenuse is 1 unit? Don’t

forget to rationalize the denominator!

5. Apply your knowledge of 30-60-90 right triangles and
identify the coordinates of point P.

6. Again, using your knowledge of 30-60-90 right triangles, identify the coordinates of point Q.

7. The cosine of 30° is ________. 8. The sine of 30° is ________.

9. The cosine of 60° is ________. 10. The sine of 60° is ________.

x

y
1

q

2a
a

30°

60°

a

45°

45°

b

b

b

11. Using your knowledge of 45-45-90 right triangles,
identify the coordinates of point R. _______

12. The cosine of 45° is ________.

13. The sine of 45° is ________.

Problem 2 – Extending the Pattern
Identify the coordinates of the following points in terms of a
and b.

14. T __________

15. U __________

16. V __________

Identify the measure of the following angles.

17. ÐWOT = _________ 18. ÐWOU = _________

19. ÐWOV = _________

Convert the following to radians:

20. 30° = _________ 21. 45° = _________

22. 60° = _________

Without converting, identify the measures of the following angles in radians.

23. ÐWOT = _________ 24. ÐWOU = _________

25. ÐWOV = _________

Elizabeth Gutermann

Elizabeth Gutermann

Elizabeth Gutermann

Elizabeth Gutermann

Elizabeth Gutermann

Elizabeth Gutermann

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