Comprehensive assessment covering reciprocal trig functions, identities, compound and double angles, t-formulas, solving equations, and inverse trig functions.
The exact value of $\cos(7\pi/6)$ is:
If $\sin(\theta) = -4/5$ and $\theta$ is in quadrant III, then $\cot(\theta)$ equals:
Which identity is equivalent to $1 + \tan^2(\theta)$?
The reciprocal of $\sin(\theta)$ is:
Using compound angles, $\cos(45^\circ - 30^\circ)$ equals:
The double-angle identity for $\tan(2\theta)$ is:
If $\tan(\theta) = 3$, then $\tan(2\theta)$ equals:
$\sin(\theta) + \sqrt{3}\cos(\theta)$ can be written as:
The t-formula substitution sets $t$ equal to:
For $0 \le \theta < 2\pi$, the equation $\cos(\theta) = -1/2$ has solutions:
For $0 \le \theta < \pi$, $\tan(3\theta) = 1$ gives how many solutions?
The principal range of $\sin^{-1}(x)$ is:
$\sin^{-1}(\sin(2\pi/3))$ equals:
The domain of $y = \cos^{-1}(x)$ is:
The range of $y = \cos^{-1}(x)$ is:
1. Find the exact value of $\cos(\frac{7\pi}{6})$. (1 mark)
2. If $\sin\theta = -\frac{4}{5}$ and $\pi < \theta < \frac{3\pi}{2}$, find $\cot\theta$. (2 marks)
3. Prove that $\tan\theta + \cot\theta = \sec\theta \csc\theta$. (2 marks)
4. Find the exact value of $\cos(15°)$. (2 marks)
5. If $\tan\theta = 3$, find $\tan(2\theta)$. (2 marks)
6. Express $\sin\theta + \sqrt{3}\cos\theta$ in the form $R\sin(\theta + \alpha)$. (3 marks)
7. Solve $2\cos^2\theta + \cos\theta - 1 = 0$ for $0 \le \theta < 2\pi$. (3 marks)
8. Solve $\tan(3\theta) = 1$ for $0 \le \theta < \pi$. (3 marks)
9. Evaluate $\sin^{-1}(\sin\frac{2\pi}{3})$. (2 marks)
10. Sketch $y = \cos^{-1}x$, labelling domain, range, and key points. (3 marks)