SAT Math Practice Question #27773 - SATify | SATify

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SAT Math Practice Question #27773 - SATify | SATify

#27773

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 $sin^{2} x + sin^{2} y \leq 1$ ?

A.

$\frac{π ^{2}}{12}$

B.

$\frac{π ^{2}}{9}$

C.

$\frac{π ^{2}}{8}$

D.

$\frac{π ^{2}}{6}$

E.

$\frac{3 π ^{2}}{16}$