Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

$3\pi \rightarrow y=2\cos \dfrac{2x}{3}\\ \\\dfrac{2\pi }{3}\rightarrow y=6\sin 3x\\ \\\dfrac{\pi }{3}\rightarrow y=-3\tan 3x\\ \\10\pi \rightarrow y=-\dfrac{2}{3}\sec \dfrac{x}{5}$

Step-by-step explanation:

The period of the functions $y=a\cos(bx+c)$ , $y=a\sin(bx+c)$, $y=a\sec (bx+c)$ or $y=a\csc(bx+c)$ can be calculated as

$T=\dfrac{2\pi}{b}$

The period of the functions $y=a\tan(bx+c)$ or $y=a\cot(bx+c)$ can be calculated as

$T=\dfrac{\pi}{b}$

A. The period of the function $y=-3\tan 3x$ is

$T=\dfrac{\pi}{3}$

B. The period of the function $y=6\sin 3x$ is

$T=\dfrac{2\pi}{3}$

C. The period of the function $y=-4\cot \dfrac{x}{4}$ is

$T=\dfrac{\pi}{\frac{1}{4}}=4\pi$

D. The period of the function $y=2\cos \dfrac{2x}{3}$ is

$T=\dfrac{2\pi}{\frac{2}{3}}=3\pi$

E. The period of the function $y=-\dfrac{2}{3}\sec \dfrac{x}{5}$ is

$T=\dfrac{2\pi}{\frac{1}{5}}=10\pi$