For , the curves (with ) and each enclose a region. Determine the value of for which…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For

0\le\theta\le\dfrac{\pi}{2}

, the curves

r=a\cos\theta

(with

a>0

) and

r=\sin\theta

each enclose a region. Determine the value of

a

for which the two enclosed regions have equal area.