graph each function using radians. 11) $y = 4sin\theta$

Explanation:

Step1: Identify amplitude

The general form of a sine - function is $y = A\sin(\theta)$, where $A$ is the amplitude. For the function $y = 4\sin(\theta)$, $A = 4$. This means the maximum value of the function is $y = 4$ and the minimum value is $y=-4$.

Step2: Find key - points

The period of the basic sine function $y=\sin(\theta)$ is $2\pi$. For $y = 4\sin(\theta)$, the period remains $2\pi$ since there is no horizontal stretch or compression ($B = 1$ in $y=A\sin(B\theta)$). We find the key - points:

• When $\theta = 0$, $y = 4\sin(0)=0$.
• When $\theta=\frac{\pi}{2}$, $y = 4\sin(\frac{\pi}{2}) = 4$.
• When $\theta=\pi$, $y = 4\sin(\pi)=0$.
• When $\theta=\frac{3\pi}{2}$, $y = 4\sin(\frac{3\pi}{2})=-4$.
• When $\theta = 2\pi$, $y = 4\sin(2\pi)=0$.

Step3: Plot the points and draw the graph

Plot the points $(0,0),(\frac{\pi}{2},4),(\pi,0),(\frac{3\pi}{2}, - 4),(2\pi,0)$ on the given coordinate grid and connect them with a smooth curve. The curve will repeat every $2\pi$ units.

Answer:

Plot the points $(0,0),(\frac{\pi}{2},4),(\pi,0),(\frac{3\pi}{2}, - 4),(2\pi,0)$ and draw a smooth sine - wave that oscillates between $y = 4$ and $y=-4$ with a period of $2\pi$.