This circle's too big!

Geometry Level 5

Find the area bound by

$x^2 + y^2 \leq 961$

$\sin(x+y) \leq 0$

Give your answer to 3 decimal places.

The answer is 1509.5.

2 solutions

Otto Bretscher
Sep 23, 2015

The area we seek is half of the area of the disk $x^2+y^2\leq{961}$ , by symmetry: If $(x,y)$ belongs to the region, then $(-x,-y)$ does not, since $\sin(-x-y)>0.$ Thus the area is $\frac{961\pi}{2}\approx\boxed{1509}$ .

Did the exact same way. BTW, can you edit your answer since the question says- "Give your answer to 3 decimal places."

Anupam Nayak - 5 years, 6 months ago

Shubham Gupta
Sep 25, 2015

X+y<=0 and the circle x²+y²=961.the line act ad a diameter the circle and the area is half of the circle.

You are wrong Gen soln is (2n-1)pi <= x+y <= (2n)pi which may include negative x but these zones when plotted out divide the circle into 2 eq halves bcoz if x +y is present then -x -y is not present

baljeet dhanoa - 5 years, 8 months ago

This circle's too big!

The answer is 1509.5.

2 solutions

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