Inverse trigonometric ranges and an expression rewritten as a single tangent

The question

Name: ______________________   Date: ____________   Inverse trigonometric ranges and an expression rewritten as a single tangent (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 $\tan^{-1}\left(-\sqrt{3}\right)$. [1 point]

2. (A(ii)) Find the exact value of $\sin^{-1}\left(\sin\frac{5\pi}{4}\right)$. [1 point]

3. (B) Rewrite $h(x)$$= \frac{\sin(2x)}{1 + \cos(2x)}$ as a single trigonometric function of $x$. Show the identities you use. [2 points]

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