Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The value of $\sin 50^\circ - \sin 70^\circ + \sin 10^\circ$ is
2. If $\tan x = -4/3$, where $x$ is in quadrant II, then $\sin(x/2)$ is
3. The value of $\cos(\frac{3\pi}{2} + x) \cos(2\pi + x) [\cot(\frac{3\pi}{2} - x) + \cot(2\pi + x)]$ is
4. The value of $\cos(\frac{\pi}{4} - x) \cos(\frac{\pi}{4} - y) - \sin(\frac{\pi}{4} - x) \sin(\frac{\pi}{4} - y)$ is
5. The maximum value of $3 \cos x + 4 \sin x + 8$ is
6. Find the value of $\sin 15^\circ$.
7. Prove that $\frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y}$.
8. Find the degree measure of 6 radians.
9. Prove that $\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$.
10. Prove that $\cot 4x (\sin 5x + \sin 3x) = \cot x (\sin 5x - \sin 3x)$.
11. Prove that $\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ = \frac{1}{16}$.
12. Case Study: The depth of water at a dock is modeled by the function $d(t) = 10 + 4 \cos(\frac{\pi t}{6})$, where $d(t)$ is in meters and $t$ is the number of hours after midnight.
    (i) Find the depth of the water at 2 AM.
    (ii) Find the maximum depth of the water.
    (iii) At what time does the first low tide occur (minimum depth)?