00:01
So we are asked for the rate at which x changes with respect to theta.
00:08
And in this situation, it's helpful to first find an equation that relates the two variables that we're concerned about.
00:17
So in this case, x and theta.
00:19
And we can easily relate them using trigonometry and looking at the figure.
00:24
You'll see that sign of theta is equal to 10.
00:32
Sorry, x over 10.
00:35
Therefore, x is equal to 10 sine theta.
00:41
Now, from this equation, if we just take the derivative of x, that is dx by d theta, that is going to be the rate at which x changes with respect to theta, and it's going to be the derivative of this.
01:05
Now, of course, you can take this constant multiple to the outside of the derivative, and we know the derivative of sine x is cos -x.
01:17
However, keep in mind, this is specifically for radiance, that that derivative is true...