Find the area of region consisting of points (x,y) which satisfy sin(x+y)=0 and x^2+y^2

Question

Find the area of region consisting of points (x,y) which satisfy sin(x+y)>=0 and x^2+y^2<=100

anonymous · Answer

x+y=npi
y=npi-x

anonymous · Answer

oh pellet..sorry

anonymous · Answer

now how will u find the area of this??

anonymous · Answer

explain more please.. :)

anonymous · Answer

what?? "Since sin(x+y)>=0 is only true for quadrants 1 and 2. You only have the top half of the circle"
what about x=5,y=-5? its in 4 quad

amistre64 · Answer

Find the area of region

consisting of points (x,y) which satisfy:

          sin(x+y) >= 0  
              x^2+y^2 <= 100

the sin function itself is between -1 and 1  and x^2+y^2 = 10 is a circle of radius 10

amistre64 · Answer

lol.... thats a cute picture :)

anonymous · Answer

hmmm

amistre64 · Answer

could we possibly convert the x^2+y^2 into a polar equation? so that we can compare the 2?

amistre64 · Answer

sin(x+y) >= 0

 sin(x)cos(y) + sin(y)cos(x) >= 0 might help?

nikvist · Answer

Sum of all regions is semicircle

nikvist · Answer

$$S=\frac{1}{2}S_{circle}=\frac{1}{2}10^2\pi=50\pi$$

anonymous · Answer

ya...but its a semicircle how will u prove?