Question

In the function f(t) = sin(t), what is the effect of multiplying t by a coefficient of 2?

changes the amplitude to 2
changes the amplitude to ½
changes the period to pi
changes the period to 4pi

Answer 1

"changes the period to pi"

Explanation:

f(t) = Sin(t),

Here, t is the period, by definition.

Multiply t by a number that is GREATER THAN 1, makes the period shorter and compressed.

Multiplying t by a number that is between 0 and 1 makes the period expanded.

For the first, if we multiply the period by a, the period becomes
`(2\pi)/(a)`

Since the problem tells us to multiply by 2, we know the period becomes compressed and becomes :

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

Third answer choice is right.