00:01
We want to find the area of the region that's inside the red circle and outside of the blue circle.
00:08
And the formula for the area between two polar functions looks like this, where the alpha theta is the farthest function from the origin, and the g of theta is the closest.
00:24
The alpha and the beta are the angles that define the region.
00:28
So for our area, if we draw a line from the origin out through our region, the outermost function, the red one is 14 cosine theta, and the innermost function would be the blue one, which is r equal 7.
00:57
And of course, we need to know the angles that define the region.
01:02
So the angle to here would be where those two functions are equal.
01:08
So if we set 14 cosine theta equal to 7, we'll have a cosine theta equals 1 .5, and the arc cosine of 1 half is pi over 3.
01:23
Now, because of symmetry, if this angle is pi over 3, then this angle would be a negative pi over 3...