Inverse trigonometric values and trigonometric equations on an interval

The question

Name: ______________________   Date: ____________   Inverse trigonometric values and trigonometric equations on an interval (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 $\cos^{-1}\left(\sin\frac{7\pi}{6}\right)$. [1 point]

2. (A(ii)) Solve $\tan^{-1}(2x - 1) = \frac{\pi}{4}$ for $x$. [1 point]

3. (B) Solve $\sin(2x) = -\frac{\sqrt{3}}{2}$ for $0 \le x \le \pi$. Show the work that leads to your answers. [2 points]

4. (C) Solve $2\sin^2 x + \sin x - 1 = 0$ for $0 \le x < 2\pi$. Show the work that leads to your answers. [2 points]