Question

What are the important points to graph `y=sin 2x`?

Answer 1

`(0, 0), (pi/4, 1), (pi/2, 0), ((3pi)/4, -1), (pi, 0)`

The graph should look something like this:
graph{sin(2x) [-2.38, 8.72, -2.907, 2.64]}

Explanation:

The equation is `y=sin2x`, so it is in the form `y=sin(b*x)` The period of this graph is `(2pi)/b`, which equals `(2pi)/2` or `pi`.
Therefore, the "important points" (quarter points) when graphing this function will be `pi/4` apart.

The amplitude of this graph is `1`, and there are no phase or vertical shifts, so the midline will be `0`, maximum `1`, and minimum `-1`.

Unshifted sine functions follow the pattern (mid, max, mid, min, max), so the `y`-coordinates will be `(0,1,0,-1,0)` And since the quarter points are `(pi/4)`, with no phase shift, the `x`-coordinates will be `(0, pi/4, pi/2, (3pi)/4, pi)`.

Combining these points, the ordered pairs will be:
`(0, 0), (pi/4, 1), (pi/2, 0), ((3pi)/4, -1), (pi, 0)`

The graph should look something like this:
graph{sin(2x) [-2.38, 8.72, -2.907, 2.64]}