Explanation
Given the function:
[tex]f(x)=2\sin x[/tex]
we can choose any value between the interval –2π < x < 2π. For example, –π, –π/2, 0, π/2, and π.
• x = –,π
[tex]f(\pi)=2\sin(\pi)=2\cdot0=0[/tex]
The coordinate is (–π, 0).
• x = –,π/2
[tex]f(-\frac{\pi}{2})=2\sin(-\frac{\pi}{2})=2\cdot-1=-2[/tex]
The coordinate is (–π/2, –2).
• x = 0
[tex]f(0)=2\cdot\sin(0)=2\cdot0=0[/tex]
The coordinate is (0, 0).
• x = ,π/2
[tex]f(\frac{\pi}{2})=2\cdot\sin(\frac{\pi}{2})=2\cdot1=2[/tex]
The coordinate is (π/2, 2).
• x = ,π
[tex]f(\pi)=2\cdot\sin(\pi)=2\cdot0=0[/tex]
The coordinate is (π, 0).
Answer
Thus, our table of values is:
Finally, graphing the points calculated in the table:
