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ACT Math : How to find the period of the sine

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Example Questions

Example Question #1 : Sine

What is the period of 2sin(4Θ)?

Possible Answers:

None of the answers are correct

$\frac{\pi}{2}$

$2\pi$

Correct answer:

$\frac{\pi}{2}$

Explanation:

The period of sinΘ is 2Π, so we set the new angle equal to the base period of 2Π and solve for Θ.

So 4Θ = 2Π and Θ = Π/2.

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Example Question #2 : Sine

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

Find the period of

$sin\, (\pi x)$ .

Possible Answers:

$\pi$

$4\pi$

$2\pi$

Correct answer:

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

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

in this case

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

which reduces to .

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Example Question #1 : How To Find The Period Of The Sine

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

Find the period of the function

$\sin \bigg(\frac{1}{2}x\bigg)$ .

Possible Answers:

$\pi$

$4\pi$

$\frac{1}{2}$

Correct answer:

$4\pi$

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

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

in this case

$\frac{2\pi}{\frac{1}{2}}=2\pi \cdot \frac{2}{1}$

which reduces to $4\pi$ .

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Example Question #4 : Sine

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

Possible Answers:

$-\pi$

$2\pi$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

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
$\frac{2\pi}{\left | 4\right |}=\frac{\pi}{2}$

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Example Question #5 : Sine

What is the period of the given trigonometric function:

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

Possible Answers:

$\frac{\pi}{3}$

$\frac{\pi}{2}$

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

$\pi$

$-\pi$

Correct answer:

$\pi$

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.

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Example Question #51 : Trigonometry

Find the period of the following formula:

$f(x)=2\sin(4\theta)$

Possible Answers:

$\frac{2}{\pi}$

$\pi$

$2\pi$

$\frac{1}{\pi}$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To find period, simply remember the following formula:

$\textup{period}=\frac{2\pi}{B}$

where B is the coefficient in front of x. Thus,

$\textup{period}=\frac{2\pi}{4}=\frac{\pi}{2}$

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ACT Math : How to find the period of the sine

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Sine

Example Question #2 : Sine

Example Question #1 : How To Find The Period Of The Sine

Example Question #4 : Sine

Example Question #5 : Sine

Example Question #51 : Trigonometry

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