Question

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

Match the functions with their periods.


Image attached.

Answer 1

:) I have to write something to submit.

Answer 2

`3\pi \rightarrow y=2\cos (2x)/(3)\\ \\(2\pi )/(3)\rightarrow y=6\sin 3x\\ \\(\pi )/(3)\rightarrow  y=-3\tan 3x\\ \\10\pi \rightarrow y=-(2)/(3)\sec (x)/(5)`

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=(2\pi)/(b)`

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

`T=(\pi)/(b)`

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

`T=(\pi)/(3)`

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

`T=(2\pi)/(3)`

C. The period of the function
`y=-4\cot (x)/(4)` is

`T=(\pi)/((1)/(4))=4\pi`

D. The period of the function
`y=2\cos (2x)/(3)` is

`T=(2\pi)/((2)/(3))=3\pi`

E. The period of the function
`y=-(2)/(3)\sec (x)/(5)` is

`T=(2\pi)/((1)/(5))=10\pi`