# Help converting triangular to polar

1. Mar 24, 2007

### dare2dream

1. The problem statement, all variables and given/known data
Find an equivalent equation in polar coordinates.

2. Relevant equations

x^2 + 4y^2 = 4

Anyone know how to do this? I don't remember how when it's an equation...=S

My best guess is (rcos theta)^2 + 4(rsin theta)^2 = 4...but that's as far as I can get.

Last edited: Mar 24, 2007
2. Mar 24, 2007

### mjsd

how do you work out the x, y projections of a vector in the 1st quadrant? think about the unit circle and how you define sin and cos... you should be able to work out the rules that relate r and $$\theta$$ to x and y.

3. Mar 25, 2007

### dare2dream

I know that r^2 = x^2 + y^2 but I don't know how to use that because of the 4 in the equation. I've thought about this problem for a week and this is as far as I've gotten. -.- (This is an equation off a take-home test we received to do over spring break.)

So r^2 = x^2 + y^2, x = rcos (theta), y = rsin (theta), and tan theta = y/x

However, knowing these, I still don't get how to figure out the problem...

Last edited: Mar 25, 2007
4. Mar 25, 2007

### mjsd

you know the answer, so all you need is rearrange (if you want) and get r on one side while the rest on the other... I don't understand your dilemma

5. Mar 25, 2007

### dare2dream

Okay...well I don't know how to do that..>.>

6. Mar 25, 2007

### cristo

Staff Emeritus
You have this (rcos theta)^2 + 4(rsin theta)^2 = 4. So expand it: $$r^2\cos^2\theta+4r^2\sin^2\theta=4$$.

Now, spot that both terms on the left contain r2, so factor this out. What do you obtain on the left hand side? Is there any way you can think of simplifying this expression you obtain?

7. Mar 25, 2007

### dare2dream

So then you get r^2 (cos^2 theta + 4 sin^2 theta) = 4

I don't know how to simplify that.

8. Mar 25, 2007

### cristo

Staff Emeritus
Well, I presume you know that sin^2(x)+cos^2(x)=1. Can you use this here?

9. Mar 25, 2007

### dare2dream

Yeah, I remember that, but I don't know what to do with the 4 then.

10. Mar 25, 2007

### cristo

Staff Emeritus
4sin^2(x)=sin^2(x)+3sin^2(x)

11. Mar 25, 2007

### dare2dream

so r^2 (1 + 3sin^2 theta) = 4?