Half-Angle Properties

There are three rules to use in these questions:

Questions

Warm-up #1. Given that sin 𝛼 = −4/5  and 𝛼 lies in quadrant IV, find the exact value of cos(𝛼/2).

For the following exercises, find the exact value using half-angle formulas.

2.  sin (𝜋/8) 

3. cos (−11𝜋/12)

4. sin (11𝜋/12)

5. cos (7𝜋/8)

6. tan (5𝜋/12)

7. tan (−3𝜋/12)

8. tan (−3𝜋/8)

For the following exercises, find the exact values of a) sin(𝑥/2), b) cos (𝑥/2), and c) tan (𝑥/2) without solving for 𝑥,  when 0° ≤ 𝑥 ≤ 360°. 

9. If tan 𝑥 = −4/3, and x is in quadrant IV.

10. If sin 𝑥 = −12/13, and 𝑥 is in quadrant III.

11.  If csc 𝑥 = 7, and 𝑥 is in quadrant II.

12. If sec 𝑥 = −4, and 𝑥 is in quadrant II.

Video For Practice if Necessary (Let me know what you think about the usefulness).