Mathematics

Problem

Let

r=2\sin\theta

with

0<\theta<\frac{\pi}{2}

. The area of the triangle formed by the origin, the positive

x

–axis, and the point

(r,\theta)

A(\theta)=\tfrac{1}{2}x y

. Determine the angle

\theta

(exact value in radians) that maximizes

A(\theta)