Determine the period and amplitude of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$.

A) period: $\frac { 2 \pi } { 13 }$; amplitude: 5

B) period: $26 \pi$; amplitude: 5

C) period: $13 \pi$; amplitude: 10

D) period: $\frac { \pi } { 13 }$; amplitude: 5

E) period: $- \frac { 2 \pi } { 13 } ;$ amplitude: $- 5$

Question

Determine the period and amplitude of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$.

A) period: $\frac { 2 \pi } { 13 }$; amplitude: 5

B) period: $26 \pi$; amplitude: 5

C) period: $13 \pi$; amplitude: 10

D) period: $\frac { \pi } { 13 }$; amplitude: 5

E) period: $- \frac { 2 \pi } { 13 } ;$ amplitude: $- 5$

Quizplus · Accepted Answer

The period of a cosine function $y = a \cos(bx + c)$ is given by $\frac{2\pi}{|b|}$. Here, $b = \frac{1}{13}$, so the period is $26\pi$. The amplitude is the absolute value of the coefficient of the cosine function, which is 5.

Determine the Period and Amplitude Of y=5cos⁡(x13+π5)y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)y=5cos(13x​+5π​)

Determine the Period and Amplitude Of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$