a) We may remember that if measures the arc distance from a point on the unit circle counterclockwise from , then gives the -coordinate of that point and gives the -coordinate.
Therefore, when , i.e, when the -coordinate of the point on the circle is the negative of its -coordinate. What fraction of the total arc length, , do these points give?
b) Points of inflection are found where and differs in sign on both sides next to the point. Extrema are found at critical points: in this case, as is differentiable and has no boundary points, at points where . To differentiate
we apply the Product Rule:
When is ? When is ? Hint: is always positive.
Hope this helps!