Question

which domain window settings would be appropriate if you wanted to graph the given function in degrees for exactly 3 periods?
$y = 4\sin(3x)$
$x\min = 0\\ \\ x\max = 3\pi$
$x\min = 0\\ \\ x\max = 120$
$x\min = -90\\ \\ x\max = 270$
$x\min = -\pi\\ \\ x\max = \pi$

Explanation:

Step1: Find period of base sine function

The base sine function $\sin(x)$ (in degrees) has a period of $360^\circ$.

Step2: Calculate period of given function

For $y = A\sin(Bx)$, period $=\frac{360^\circ}{|B|}$. Here $B=3$, so:
$\text{Period} = \frac{360^\circ}{3} = 120^\circ$

Step3: Find total range for 3 periods

Total span for 3 periods: $3 \times 120^\circ = 360^\circ$. Starting at $0^\circ$, the upper limit is $360^\circ$. Now check the options:

• Option 1: $X\text{max}=3\pi$ is radians, not degrees.
• Option 2: $X\text{max}=120^\circ$ is only 1 period.
• Option 3: Total span $=270^\circ - (-90^\circ)=360^\circ$, which is 3 periods.
• Option 4: Uses radians, not degrees.

Answer:

X min = -90 X max = 270