graph the function.\n$f(x)=sinleft(\frac{pi x}{2}\right)$\nuse the sine tool. first plot a point on the mid…

graph the function.\n$f(x)=sinleft(\frac{pi x}{2}\right)$\nuse the sine tool. first plot a point on the mid - line of the function. then plot either the maximum or minimum point closest to the first point plotted.\nsine undo redo × reset

graph the function.\n$f(x)=sinleft(\frac{pi x}{2}\right)$\nuse the sine tool. first plot a point on the mid - line of the function. then plot either the maximum or minimum point closest to the first point plotted.\nsine undo redo × reset

Answer

Explanation:

Step1: Find mid - line point

The mid - line of $y = \sin(\frac{\pi x}{2})$ is $y = 0$. Let $\frac{\pi x}{2}=0$, then $x = 0$. So a point on the mid - line is $(0,0)$.

Step2: Find max/min point

The general form of a sine function is $y = A\sin(Bx - C)+D$. For $y=\sin(\frac{\pi x}{2})$, $A = 1$, $B=\frac{\pi}{2}$, $C = 0$, $D = 0$. The period $T=\frac{2\pi}{B}=\frac{2\pi}{\frac{\pi}{2}}=4$. The maximum value of $\sin(\frac{\pi x}{2})$ is 1 when $\frac{\pi x}{2}=\frac{\pi}{2}+2k\pi,k\in\mathbb{Z}$, solving for $x$ gives $x = 1 + 4k$. The minimum value of $\sin(\frac{\pi x}{2})$ is - 1 when $\frac{\pi x}{2}=\frac{3\pi}{2}+2k\pi,k\in\mathbb{Z}$, solving for $x$ gives $x = 3+4k$. The maximum point closest to $(0,0)$ is $(1,1)$.

Answer:

Plot the point $(0,0)$ on the mid - line and the point $(1,1)$ (a maximum point).