Developing the Unit Circle, Part 1 Name ___________________________

Period ___________________________

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

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

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