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ACT Math : How to find the period of the cosine

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Example Questions

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

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

$cos\, (2x)$ .

Possible Answers:

$\pi$

$2\pi$

$\pi+2$

Correct answer:

$\pi$

Explanation:

For the function

cos(Ax)

the period is equal to

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

or in this case

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

which reduces to $\pi$ .

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

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

$\cos \bigg(\frac{1}{4}\pi x\bigg)$ .

Possible Answers:

$4\pi$

$8\pi$

Correct answer:

Explanation:

For the function

cos(Ax)

the period is equal to

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

or in this case

$\frac{2\pi}{\frac{1}{4}\pi}=2\pi \cdot \frac{4}{1\pi}$

which reduces to .

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Example Question #3 : How To Find The Period Of The Cosine

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

$cos\, (\pi x)$ .

Possible Answers:

$2\pi$

$\pi$

Correct answer:

Explanation:

For the function

cos(Ax)

the period is equal to

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

or in this case

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

which reduces to .

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Example Question #4 : How To Find The Period Of The Cosine

A function with period will repeat its solutions in intervals of length .

What is the period of the function f(x) = cos(x) +3 ?

Possible Answers:

$3\pi$

$2\pi$

$\frac{2\pi}{3}$

Correct answer:

$2\pi$

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for f(x) = cos(x) +3 , $P = \frac{2\pi}{1} = 2\pi$ .

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Example Question #5 : How To Find The Period Of The Cosine

A function with period will repeat its solutions in intervals of length .

What is the period of the function $f(x) = 3cos(4\pi x-4) -2$ ?

Possible Answers:

$4\pi$

$\frac{\pi}{2}$

$8\pi^2$

$\frac{1}{2}$

$2\pi$

Correct answer:

$\frac{1}{2}$

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for $f(x) = 3cos(4\pi x-4) -2$ , $P = \frac{2\pi}{4\pi} = \frac{1}{2}$ .

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Example Question #6 : How To Find The Period Of The Cosine

A function with period will repeat its solutions in intervals of length .

What is the period of the function $f(x) = 2cos(\frac{1}{2}\pi x)$ ?

Possible Answers:

$\pi$

$4\pi$

$2\pi$

Correct answer:

Explanation:

For a trigonometric function $f(x) = \alpha cos(bx -c) +d$ , the period is equal to $\frac{2\pi}{b}$ . So, for $f(x) = 2cos(\frac{1}{2}\pi x)$ , $P = \frac{2\pi}{\frac{1}{2}\pi} = 4$ .

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ACT Math : How to find the period of the cosine

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

Example Question #3 : How To Find The Period Of The Cosine

Example Question #4 : How To Find The Period Of The Cosine

Example Question #5 : How To Find The Period Of The Cosine

Example Question #6 : How To Find The Period Of The Cosine

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