Question

How do you use cosine rule to sketch y = sin 3x without technology?

Answer 1

It's 4.5 periods of a sine wave with the axes labeled appropriately.

Explanation:

I edited the question to match the link.

I'm not sure which cosine rule you mean, but to sketch

`y=sin 3x`

you just sketch

`y = sin x`

Don't draw anything yet. We need to figure out how much to draw.

We're to sketch from `x=0` to `3pi` which means the argument to the sine wave goes from `0` to `9 pi` because it's multiplied by three. That means we need four and half periods of the sine wave, because the period of `sin x` is `2pi`.

Now we can draw the axes and `4 1/2` periods of a sine wave the usual way, starting from the origin and off to the right.

The zero crossings of `sin 3x` will be at `0, pi/3, {2pi}/3, pi, ...`. Label the x axis at those points.

We're not scaling or adding to the sin, so the y axis will have the usual +1 for the maximum of the sine wave and -1 for the minimum. Label the y axis.

Socratic's grapher doesn't write the `pi`s in but you should.

graph{y = sin(3x) + 0 sqrt(x) [-0.307, 9.42, -2, 2]}