How to find the period of the cosine

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ACT Math › How to find the period of the cosine

Questions 1 - 6

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

What is the period of the function ?

$2\pi$

$3\pi$

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

Explanation

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

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

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

$\frac{1}{2}$

$\frac{\pi}{2}$

$2\pi$

$4\pi$

$8\pi^2$

Explanation

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

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

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

$4\pi$

$\pi$

$2\pi$

Explanation

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