Question

convert to polar form. x^2=8y

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

right

Answer 5

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

Answer 6

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

Answer 7

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?

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

half angle

Answer 12

cos(A/2)

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

you use the one that matches, double angle.

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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!

Answer 22

You're welcome