How can I find the area inside two polar curves?

[G01]

I need to find the area that's inside both of the following curves:

r = \sin\theta

r = \cos\theta

I know that I should have to subtract the area of the one curve from the other and I know the area formula for polar coordinates, but I just can't see how to set this one up any help or hints would be appreciated.

 

[ToxicBug]

It's just two circles. the sin one is centered on the y-axis and the cos one is centered on the x axis. Sketch them and you will see what you have to do. Because of symmetry, you only need to integrate sin(t) from t=0 to t=pi/4 and multiply that integral by 2. Integrating cos(t) from t=pi/4 to t=pi/2 and then multiplying that integral by 2 will give you the same exact result.

 

[G01]

Shouldn't the area of sin t from 0 to pi/4 cover everything from the curve to the y axis. If you multiply that by 2 then you will end up with more area than what's in the loop won't you? I'm sorry I must be really confused

 

[ToxicBug]

No, that's 0 to pi/2. pi/4 is 1/8th of a circle

 

[G01]

these circles complete one rotation every pi degrees remember. So Pi/4 would be at the top of the circle with the cos and at the side of the sine circle.

 

[ToxicBug]

Dude, why are you arguing with me? I said that you integrate sin(t) from 0 to pi/4. If you don't think my answer is right, then don't use it.

 

[G01]

Im sorry, I think my explanation of this problem was bad I'm going to try to explain it again in another thread so I you still feel like halping me please go there.