find the period and amplitude.\ny = 6/7 cos(πx/4)\nperiod\namplitude\nneed help? read it\nsubmit answer\n-/2…

Explanation:

Step1: Recall amplitude - formula for $y = A\cos(Bx)$

For the function $y=\frac{6}{7}\cos(\frac{\pi x}{4})$, the amplitude $A$ is given by the absolute - value of the coefficient of the cosine function. $A = \left|\frac{6}{7}\right|=\frac{6}{7}$

Step2: Recall period - formula for $y = A\cos(Bx)$

The period $T$ of the function $y = A\cos(Bx)$ is $T=\frac{2\pi}{|B|}$. Here, $B=\frac{\pi}{4}$, so $T=\frac{2\pi}{\frac{\pi}{4}}$. $T = 2\pi\times\frac{4}{\pi}=8$

Step3: Recall amplitude - formula for $y = A\sin(Bx)$

For the function $y=-6\sin(\frac{\pi x}{5})$, the amplitude $A$ is given by the absolute - value of the coefficient of the sine function. $A = | - 6| = 6$

Step4: Recall period - formula for $y = A\sin(Bx)$

The period $T$ of the function $y = A\sin(Bx)$ is $T=\frac{2\pi}{|B|}$. Here, $B = \frac{\pi}{5}$, so $T=\frac{2\pi}{\frac{\pi}{5}}$. $T=2\pi\times\frac{5}{\pi}=10$

Answer:

For $y=\frac{6}{7}\cos(\frac{\pi x}{4})$: period: $8$ amplitude: $\frac{6}{7}$ For $y=-6\sin(\frac{\pi x}{5})$: period: $10$ amplitude: $6$