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

Question

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

1 Answer

Impact of this question

1208 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-18T11:53:40

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

$y = sin 3 x$ $y=sin 3x$

you just sketch

$y = sin x$ $y = sin x$

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

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

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

The zero crossings of $sin 3 x$ $sin 3x$ 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]}

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question