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- anonymous

convert to polar form. x^2=8y

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- anonymous

convert to polar form. x^2=8y

- chestercat

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- anonymous

x=rcos(theta) y=rsin(theta)

- anonymous

r^2cos^2(theta)=8rsin(theta)

- anonymous

so its r=8sin(theta)/cos^2(theta)?

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- anonymous

right

- anonymous

so the answer is in r= form when there are no set points. But with set points you write it as (r, theta) ?

- anonymous

I don't know what you mean by set points. In polar form there is a magnitude and a direction/angle.

- anonymous

and i'd rather not write up a new question for these, but im also struggling the other way around. converting polar to rectangular.
1) r^2*cos(2theta)=1
2)r=2cos(theta)-4sin(theta)
think you can help out?

- anonymous

by set points in meant (1,4) or something to that extent. I was able to answer that though.

- anonymous

when you run into something with a coefficient of theta use your trig identities to get rid of it so you can use x=rcos(theta) y=rsin(theta) to convert back to rectangular.

- anonymous

actually i have 2. and what trig identity would i use here?
cos(2A) = cos²A − sin² ?

- anonymous

half angle

- anonymous

cos(A/2)

- anonymous

im not sure how this applies if i have r^2 * cos(2*theta)

- anonymous

cos(theta/2)= sqrt((1+cos(theta))/2)

- anonymous

actually you were right, you don't use the half angle...

- anonymous

you use the one that matches, double angle.

- anonymous

there are 3 for cosine, i cant tell which one would work in this scenario

- anonymous

cos(2a)=cos^2*a)+sin^2(a)

- anonymous

when you put that one in you'll end up with two terms both multiplied by r^2

- anonymous

then you can simply substitute them for x^2 and y^2

- anonymous

so I'm at r^2cos^2(theta)- r^2sin^2(theta)=1. which turns to x^2-y^2=1...and thats the answer on the sheet. Got it, thanks!

- anonymous

You're welcome

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