HSC Mathematics Advanced trigonometric functions quiz

150°

120°

135°

165°

$3\pi$ cm²

$6\pi$ cm²

$12\pi$ cm²

$\pi$ cm²

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$-\frac{1}{2}$

$-\frac{\sqrt{3}}{2}$

$\frac{3}{2\pi}$

$\frac{2\pi}{3}$

$\frac{2\pi}{9}$

$\frac{\pi}{3}$

Amplitude 2, period $2\pi$, phase shift $\frac{\pi}{4}$ right, midline $y = 1$

Amplitude 1, period $\pi$, phase shift $\frac{\pi}{4}$ left, midline $y = 2$

Amplitude 2, period $\pi$, phase shift $\frac{\pi}{4}$ left, midline $y = 1$

Amplitude 2, period exactly $2\pi$, phase shift $\frac{\pi}{4}$ left, midline $y = 1$

$\frac{4}{5}$

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{4}{5}$

1

2

3

4

$\theta = 0, \pi, 2\pi$ only

$\theta = \frac{\pi}{3}, \frac{5\pi}{3}$ only

$\theta = 0, \frac{\pi}{3}, \pi, \frac{5\pi}{3}, 2\pi$

$\theta = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$

$\frac{1}{\sin\theta}$

$\frac{\cos\theta}{\sin\theta}$

$\frac{1}{\tan\theta}$

$\frac{1}{\cos\theta}$

7 m at $t = 3$

5 m at $t = 0$

7 m at $t = 6$

2 m at $t = 3$

$2\sin\theta\cos\theta$

$1 + 2\sin^2\theta$

$2\cos^2\theta - 1$

$\sin^2\theta - \cos^2\theta$

$1 - \cos\theta$

$\sin\theta + \cos\theta$

$\tan\theta$

$1 + \cos\theta$

$[-7, -1]$

$[-3, 3]$

$[-1, 7]$

$[-12, 4]$

$\theta = \frac{\pi}{4}, \frac{5\pi}{4}$

$\theta = \frac{3\pi}{4}, \frac{7\pi}{4}$

$\theta = \frac{3\pi}{4}, \frac{5\pi}{4}$

$\theta = \frac{\pi}{4}, \frac{3\pi}{4}$