FP2 polar coordinates

C1 has the equation : r= (root)3 sin(2theta) 0<theta< pi/2

C2 has the equation : r= 3cos (2theta) 0 < theta < pi/4

how do you work out the area R??

they meet at pi/6

I did

(0.5 (intergral) (C2)^2 (with limits pi/4 to 0)) - (0.5 (intergral) (C1)^2 ( with limits pi/4 to pi/6)

i got the wrong answer :/ need help please

thanks a lot :colondollar:

Reply 1

user2020user

The area is given by the following equality, where

\phi

is the value of

\theta

for which the polar curves intersect and

r_n

denotes the polar curve of

C_n

, where

n=1, 2

\displaystyle \mathbf{R} = \dfrac{1}{2} \int_{0}^{\phi} \left( r_2 \right)^2 \text{d}\theta - \dfrac{1}{2} \int_{0}^{\phi} \left( r_1 \right)^2 \text{d}\theta

(edited 9 years ago)

Reply 2

mr.dowell

Original post by Khallil

The area is given by the following equality, where

\phi

is the value of

\theta

for which the polar curves intersect and

r_n

denotes the polar curve of

C_n

, where

n=1, 2

\displaystyle \mathbf{R} = \dfrac{1}{2} \int_{0}^{\phi} \left( r_2 \right)^2 \text{d}\theta - \dfrac{1}{2} \int_{0}^{\phi} \left( r_1 \right)^2 \text{d}\theta

Omg is that all?

So is that always the case when they intersect? The area of the intersections of the 2 curves is given by that formula?

Thank you so much :smile:

Reply 3

user2020user

Original post by mr.dowell

...

That's just for this example I think. It's always much better to look at the given curves in each question as loads of different cases arise when you're asked to find different types of areas.