Questions covered in Basic

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 radian measure of $240^\circ$ is
2. The value of $\sin \frac{31\pi}{3}$ is
3. If $\cos x = -1/2$ and $x$ lies in the third quadrant, then $\sin x$ is
4. The value of $\tan 15^\circ$ is
5. The range of $f(x) = \cos x$ is
6. Find the degree measure corresponding to $\frac{11}{16}$ radians (Use $\pi = 22/7$).
7. Find the value of $\sin 75^\circ$.
8. Prove that $\frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y}$.
9. Prove that $\frac{\cos 7x + \cos 5x}{\sin 7x - \sin 5x} = \cot x$.
10. Find the value of $\tan \frac{13\pi}{12}$.
11. Prove that $\cos 6x = 32 \cos^6 x - 48 \cos^4 x + 18 \cos^2 x - 1$.
12. Case Study: A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes 88 meters when it traces an angle of $72^\circ$ at the center.
    (i) Find the length of the rope (radius).
    (ii) If the angle was $36^\circ$, what would be the arc length?