# Homework Help: Area inside two polar curves

1. May 13, 2006

### G01

I need to find the area thats 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.

2. May 13, 2006

### 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.

3. May 13, 2006

### 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 whats in the loop won't you? I'm sorry I must be really confused

4. May 13, 2006

### ToxicBug

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

5. May 13, 2006

### 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.

6. May 13, 2006

### 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.

7. May 14, 2006

### G01

Im sorry, I think my explaination 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.