The period of the function $f ( x ) = - \frac { 2 } { 3 } + 2 \cos ( 3 x - 4 )$ is

A) $\frac { \pi } { 3 }$
B) $\frac { 2 \pi } { 3 }$
C) $2 \pi$
D) $4 \pi$
E) $6 \pi$

Question

The period of the function $f ( x ) = - \frac { 2 } { 3 } + 2 \cos ( 3 x - 4 )$ is

A) $\frac { \pi } { 3 }$
B) $\frac { 2 \pi } { 3 }$
C) $2 \pi$
D) $4 \pi$
E) $6 \pi$

Quizplus · Accepted Answer

The period of a cosine function is given by $ \frac{2\pi}{|b|} $, where $b$ is the coefficient of $x$ inside the cosine function. Here, $b = 3$, so the period is $ \frac{2\pi}{3} $. The constants outside the cosine function do not affect the period.

The Period of the Function f(x)=−23+2cos⁡(3x−4)f ( x ) = - \frac { 2 } { 3 } + 2 \cos ( 3 x - 4 )f(x)=−32​+2cos(3x−4)

The Period of the Function $f ( x ) = - \frac { 2 } { 3 } + 2 \cos ( 3 x - 4 )$