Question

consider the function y = 2sin(x) for 0° ≤ x ≤ 360°. graph the function: plot the function y = 2sin(x) on a coordinate plane. label the x - axis as \angle (degrees)\ and the y - axis as \y - value\. mark the coordinates of all key points where the graph intersects the x - axis, reaches a maximum, or minimum within the given interval.

Explanation:

Step1: Recall sine - function properties

The general form of a sine function is $y = A\sin(Bx - C)+D$. For $y = 2\sin(x)$, $A = 2$, $B = 1$, $C = 0$, $D = 0$. The amplitude is $|A|=2$, and the period is $T=\frac{2\pi}{B}=360^{\circ}$ (since $B = 1$).

Step2: Find x - intercepts

Set $y = 0$. So, $2\sin(x)=0$. Then $\sin(x)=0$. In the interval $0^{\circ}\leq x\leq360^{\circ}$, $x = 0^{\circ},180^{\circ},360^{\circ}$. The coordinates of the x - intercepts are $(0,0),(180,0),(360,0)$.

Step3: Find maximum and minimum points

The amplitude of $y = 2\sin(x)$ is 2. The maximum value of $\sin(x)$ is 1 and the minimum is - 1. When $\sin(x)=1$, $x = 90^{\circ}$ and $y=2$ (coordinate $(90,2)$). When $\sin(x)= - 1$, $x = 270^{\circ}$ and $y=-2$ (coordinate $(270, - 2)$).

Answer:

• X - intercepts: $(0,0),(180,0),(360,0)$
• Maximum point: $(90,2)$
• Minimum point: $(270, - 2)$