SOLUTION: Please help me with that question . Find the area of the region lies inside curve and outside the second curve . r=10sin theta; , r=5

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Question 1074558: Please help me with that question .
Find the area of the region lies inside curve and outside the second curve . r=10sin theta; , r=5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the points of intersection, you can read it off the graph or solve.
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10sin%28theta%29=5
sin%28theta%29=1%2F2
theta=30 and theta=150
So then,
A=int%28%281%2F2%29%28%2810sin%28theta%29%29%5E2-5%5E2%29%2Cd%28theta%29%2C30%2C150%29
A=25x-50sin%28x%29cos%28x%29%2BC
Convert the angles to radians,
30%2A%28%282pi%29%2F360%29=pi%2F6
150%2A%28%282pi%29%2F360%29=%285%2F6%29pi
So,

2A=25pi%284%2F6%29%2B43.30127
2A=52.35988%2B43.30127
2A=95.66
So,
A=47.83