Question

Convert polar eq. to rectangular
cos2(Theta)=-1

Answer 1

@zepdrix

Answer 2

@sdfgsdfgs

Answer 3

@rvc

Answer 4

@perl

Answer 5

Is that a square on the cosine? :)

Answer 6

Nope, it's\[\cos2(\theta)=-1\]

Answer 7

Recall your Double Angle Formula for Cosine? :)

Answer 8

\[\cos^2(\theta)-\sin^2(\theta)=-1\]

Answer 9

Wait, we're going to rectangular? 0_o
but no r?
Hmm interesting lol

Answer 10

yeah that's what's weird! xD
I've tried multiplying r in but it gets pretty sketchy.

Answer 11

How bout we... multiply both by r^2

Answer 12

\[\Large\rm (r \sin \theta)^2-(r \cos \theta)^2=1\]I combined a few steps into one here, ok with this? :o

Answer 13

Crappp my game is starting >.<

Answer 14

ai, do you need to go?

Answer 15

Woops typo,\[\Large\rm (r \sin \theta)^2-(r \cos \theta)^2=r^2\]

Answer 16

Yah :c
Do you see how I got here?
Can you continue from there maybe? :3

Answer 17

Hm, I'm not sure. But i'll work it out. You can go! thanks :)

Answer 18

ok ill come back later if needed c:

Answer 19

okies. but the r on the right side would be negative, yeah?

Answer 20

@alekos

Answer 21

This is the question
$$\Large \cos(2\theta) = -1$$

Answer 22

yep

Answer 23

We can use trig substitution
$$
\Large{ \cos(2\theta) = -1
\\ 2\cos^2\theta -1 = -1
}
$$

Answer 24

Okay, sounds good..

Answer 25

\[2\cos^2(\theta)=0\] simplify?

Answer 26

correct

Answer 27

We can use trig substitution
$$
\Large{ \cos(2\theta) = -1
\\ 2\cos^2\theta -1 = -1
\\ 2\cos^2\theta = 0
\\ \cos^2\theta = 0
\\ \cos\theta = 0
\\ \theta = \arccos(0)
\\ \theta = \frac{\pi }{2}
}
$$
now it is true that in polar to rectangular
theta = arctan(y/x)

Answer 28

actually that is the y axis, if you graph it

Answer 29

so the rectangular equation is x = 0

Answer 30

oo yes this makes sense.