find the amplitude and period of each function. then graph the function. 1. y = 4 sin θ 3. y = cos 2θ

Explanation:

Step1: Recall amplitude formula for $y = A\sin\theta$

For the function $y = A\sin\theta$, the amplitude is $|A|$. For $y = 4\sin\theta$, $A = 4$, so the amplitude $a_1=|4| = 4$. The period of $y=\sin\theta$ is $2\pi$, and for $y = A\sin\theta$ the period remains $T_1 = 2\pi$.

Step2: Recall amplitude and period formula for $y=\cos(B\theta)$

For the function $y=\cos(B\theta)$, the amplitude is $|1| = 1$ (since the coefficient of $\cos$ is 1). The period formula is $T=\frac{2\pi}{|B|}$. For $y=\cos(2\theta)$, $B = 2$, so the period $T_2=\frac{2\pi}{|2|}=\pi$.

Answer:

For $y = 4\sin\theta$: Amplitude is 4, Period is $2\pi$. For $y=\cos(2\theta)$: Amplitude is 1, Period is $\pi$.