Question

graph the trigonometric function.
$y=\frac{3}{2}\sin\left(\frac{1}{2}x\
ight)$
plot all points corresponding to x-intercepts, minima, and maxima within one cycle. then click on the graph-a-function button.

Explanation:

Step1: Identify amplitude and period

Amplitude = 3/2, period = 4π (since period = 2π/(1/2) = 4π)

Step2: Find x-intercepts

Set sin(1/2 x)=0 → 1/2 x=0, π, 2π → x=0, 2π, 4π → points (0,0), (2π,0), (4π,0)

Step3: Find maxima

sin(1/2 x)=1 → 1/2 x=π/2 → x=π → y=3/2 → point (π, 3/2)

Step4: Find minima

sin(1/2 x)=-1 →1/2 x=3π/2 →x=3π →y=-3/2 →point (3π, -3/2)

Answer:

Key points within one cycle: (0, 0), (π, 3/2), (2π, 0), (3π, -3/2), (4π, 0)