Determine the period and amplitude of the following function.
$y=4 \cos \left(\frac{3 x}{4}+\frac{\pi}{4}\right)$

A) period: $2 \pi$, amplitude : 2
B) period: $10 \pi$, amplitude : 2
C) period: $5 \pi$, amplitude : 4
D) period : $\frac { 8 \pi } { 3 } ;$ amplitude $: 4$
E) period: $3 \pi$, amplitude : 4

Question

Determine the period and amplitude of the following function.
$y=4 \cos \left(\frac{3 x}{4}+\frac{\pi}{4}\right)$

A) period: $2 \pi$, amplitude : 2 
B) period: $10 \pi$, amplitude : 2 
C) period: $5 \pi$, amplitude : 4 
D) period : $\frac { 8 \pi } { 3 } ;$ amplitude $: 4$ 
E) period: $3 \pi$, amplitude : 4

Quizplus · Accepted Answer

The period of the function is given by $\frac{2\pi}{\left|\frac{3}{4}ight|}=\frac{8\pi}{3}$ (recall that the period of $\cos(ax)$ is $\frac{2\pi}{|a|}$). The amplitude is simply the coefficient in front of the cosine function, which is $4$. Therefore, the answer is $\boxed{	extbf{(D) } 	ext{ period : } \frac { 8 \pi } { 3 } ; 	ext{ amplitude : } 4}$.

Determine the Period and Amplitude of the Following Function y=4cos⁡(3x4+π4)y=4 \cos \left(\frac{3 x}{4}+\frac{\pi}{4}\right)y=4cos(43x​+4π​)

Determine the Period and Amplitude of the Following Function $y=4 \cos \left(\frac{3 x}{4}+\frac{\pi}{4}\right)$