Need Guidance: Area in between Polar Curves

  • Thread starter GavinMath
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  • #1
GavinMath
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Homework Statement



Find the area of the region that lies inside both of the circles
r = 2sin(x)
r = sin(x) + cos(x)

Homework Equations



A = (1/2)(int from a to b): r^2 dx

(I apologize because I do not know how to make calculus look proper in text form)

The Attempt at a Solution



What I need is some theoretical help. Through graphing these circles I can see that they intersect at pi/4. However, I see that they intersect near the origin, however I can not get a common angle, which makes me confused on how to set up the intervals of my integration. Any ideas to get me going would be much appreciated!
 

Answers and Replies

  • #2
36,713
8,713

Homework Statement



Find the area of the region that lies inside both of the circles
r = 2sin(x)
r = sin(x) + cos(x)

Homework Equations



A = (1/2)(int from a to b): r^2 dx

(I apologize because I do not know how to make calculus look proper in text form)

The Attempt at a Solution



What I need is some theoretical help. Through graphing these circles I can see that they intersect at pi/4. However, I see that they intersect near the origin, however I can not get a common angle, which makes me confused on how to set up the intervals of my integration. Any ideas to get me going would be much appreciated!

What about setting the r values in the two equations equal, and solving for the angle?
 

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