Question

A nick on the edge of a CD rotates to (−6, 5) during one song when represented graphically. What is the sine value of this function?

Answer 1

Hi! Hopefully I can help with a a little direction.

The CD spins around its center, so any point on it is going around in a circle - including the nick on the edge. Now I'll \(\it assume\) that \((0,0)\) is the center of the CD. The question didn't say that, but we have a circle and we typically have circles centered on the origin to make the equation easier. It would be kind of the problem to say that, but ah well.

So this nick is going around in the path of a circle that is centered around the origin.

So, I think that that is the function. It's not something you need to have explicitly.

The sign function is a function of an angle (that we're not using) and gives you the ratio of the y-component to the radial component of a circle of radius of 1 that happens to be centered at the origin.

So, I think that you want to find the ratio of the y-component to the radial component.


The y-component... Well you have the y-coordinate, so that's it.

The radial component can come from the Pythagorean theorem. Notice that it will be positive despite a negative x-component. (\(\sqrt{a^2+b^2}=c^2\))

So, to get the ratio, it's the y-component divided by the radial component that you'll find - that's the sine value in a nutshell.

Good luck!