# Help converting triangular to polar

## Homework Statement

Find an equivalent equation in polar coordinates.

## Homework 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.

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## Answers and Replies

mjsd
Homework Helper
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.

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...

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

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

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

cristo
Staff Emeritus
Science Advisor
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?

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

I don't know how to simplify that.

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

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

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

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