How to find the period of the sine

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ACT Math › How to find the period of the sine

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What is the period of the function $f(t) = -2\sin(4t)$ ?

$\frac{\pi}{2}$

CORRECT

$-\pi$

$2\pi$

Explanation

To find the period of Sine and Cosine functions you use the formula:
$\frac{2\pi}{\left | b\right |}$ where comes from $f(t) = a\sin(bt)$ . Looking at our formula you see b is 4 so
$\frac{2\pi}{\left | 4\right |}=\frac{\pi}{2}$

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of

$sin, (\pi x)$ .

CORRECT

$\pi$

$4\pi$

$2\pi$

Explanation

For the function

the period is equal to

$\frac{2\pi}{A}$

in this case

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

which reduces to .

What is the period of the given trigonometric function:

$c(t) = 3\sin(-2t)$ . Leave your answer in terms of $\pi$ , simplify all fractions.

$\pi$

CORRECT

$-\pi$

$\frac{\pi}{2}$

$-\frac{\pi}{2}$

$\frac{\pi}{3}$

Explanation

To find the period of a sine, cosine, cosecant, or secant funciton use the formula:

$\omega = \frac{2\pi}{\left|b\right|}$ where comes from the general formula: $c(t)=a\sin(bt)$ . We see that for our equation $\left|b\right| = 2$ and so the period is $\pi$ when you reduce the fraction.