Question

write the equation of a sine function with amplitude = 7 and period = $2\pi$.
type the equation in the form $y = a\sin(\omega x)$ or $y = a\cos(\omega x)$ with $\omega > 0$. select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.

Explanation:

Step1: Identify amplitude A

The amplitude is given as 7, so $A = 7$.

Step2: Calculate angular frequency $\omega$

Use period formula $T=\frac{2\pi}{\omega}$. Given $T=2\pi$, solve for $\omega$:
$$\omega=\frac{2\pi}{T}=\frac{2\pi}{2\pi}=1$$

Step3: Write sine function

Substitute $A=7$ and $\omega=1$ into $y=A\sin(\omega x)$.

Answer:

$y = 7\sin(x)$