Inverse cosine values and a sum rewritten as a single sine term

The question

Name: ______________________   Date: ____________   Inverse cosine values and a sum rewritten as a single sine term (6 points)

No calculator. Give exact values, use radians, and show the work for each part. Only real solutions are asked for.

1. (A(i)) Find the exact value of $\sin\left(\cos^{-1}\left(-\frac{3}{5}\right)\right)$. [1 point]

2. (A(ii)) Solve $\cos^{-1}(x) = \frac{5\pi}{6}$ for $x$. [1 point]

3. (B) Rewrite $k(x)$$= \sin\left(x + \frac{\pi}{6}\right)$$+ \sin\left(x - \frac{\pi}{6}\right)$ as a single term of the form $a\sin x$. Show the identities you use. [2 points]

4. (C) Solve $k(x) = \frac{3}{2}$ for $0 \le x < 2\pi$. [2 points]