SAT Math Practice Question #27772 - SATify | SATify

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SAT Math Practice Question #27772 - SATify | SATify

#27772

geometry

trigonometry

area

Calculus

hard

120 sec

Let $S$ be the set of all points $(x, y)$ in the coordinate plane such that $0 \leq x \leq \frac{π}{2}$ and $0 \leq y \leq \frac{π}{2}$ . What is the area of the subset of $S$ for which $cos (x - y) \geq \frac{1}{2}$ ?

A.

$\frac{π ^{2}}{4}$

B.

$\frac{π ^{2}}{6}$

C.

$\frac{π ^{2}}{3}$

D.

$\frac{2 π ^{2}}{9}$

E.

$\frac{5 π ^{2}}{18}$