You are Here: Home >< Maths

# Finding the area between two polar graphs Watch

1. I need to find the area between r^2 = sin(2theta) and r^2= cos(2theta)...I graphed them, but I'm not sure about the intervals...I tried pi/4 and 0 and then multiplied the answer by two, but it didn't work. So how will I know the intervals? Do I just find the point of intersection?

2. I hope I can describe this OK.

The two graphs are like double-loops, at an angle of 45 degrees to each other. Centred on the origin.

There are two areas of overlap. One in the1st quadrant and one in the 3rd quadrant.

Draw a line y = mx through the intersection points. This line will bisect each of the two areas of overlap.

Now find the area under the curve r^2=cos*2t in the 1st quadrant. Also find the area under the same curve from t = 0 to t = atan(m).

Subtract these areas.

Multiply by 4.
3. (Original post by steve10)
I hope I can describe this OK.

The two graphs are like double-loops, at an angle of 45 degrees to each other. Centred on the origin.

There are two areas of overlap. One in the1st quadrant and one in the 3rd quadrant.

Draw a line y = mx through the intersection points. This line will bisect each of the two areas of overlap.

Now find the area under the curve r^2=cos*2t in the 1st quadrant. Also find the area under the same curve from t = 0 to t = atan(m).

Subtract these areas.

Multiply by 4.
Shouldn't it be from theta=0 to theta=pi/4 ?
4. The 1st area I mentioned, under the curve r^2=cos*2t in the 1st quadrant, is from theta = 0 to pi/4.

The 2nd area is from 0 to atan(m), where m is the slope of the bisecting line. You have to figure out m yourself from the intersection of the two curves.
Attached Images

5. Lol this is my day job

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 30, 2010
Today on TSR

### Degrees to get rich!

... and the ones that won't

### Women equal with Men?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.