Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = 8 \cos ( 2 x + 1 ) - \sin ( 3 x - 1 )$$
A) $2 \pi$
B) Not periodic
C) $\pi$
D) $4 \pi$

Question

Quizplus · Accepted Answer

The function is periodic because both cosine and sine functions are periodic. The period of $\cos(2x+1)$ is $\pi$, and the period of $\sin(3x-1)$ is $\frac{2\pi}{3}$. The least common multiple of these periods is $2\pi$, making the entire function periodic with a period of $2\pi$.

Determine Whether the Function Is Periodic f(x)=8cos⁡(2x+1)−sin⁡(3x−1)f ( x ) = 8 \cos ( 2 x + 1 ) - \sin ( 3 x - 1 )f(x)=8cos(2x+1)−sin(3x−1)

Determine Whether the Function Is Periodic $f ( x ) = 8 \cos ( 2 x + 1 ) - \sin ( 3 x - 1 )$