Rewrite polar equation as Cartesian (trig identities)

[craig16]

Homework Statement

x=2acos(theta- pi/3)cos(theta)
y=2acos(theta- pi/3)sin(theta)

Write everything in terms of x and y

Homework Equations

cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
sina/cosa=tana

etc...

The Attempt at a Solution

I've tried a lot of rearranging, can't figure it out.

 

[summerwind]

I'm not sure I understand. Are you trying to write \theta\ and a in terms of x and y?

If so, take a look at x/y or y/x.

 

[I like Serena]

Homework Statement

x=2acos(theta- pi/3)cos(theta)
y=2acos(theta- pi/3)sin(theta)

Write everything in terms of x and y

You'll be able to make good use of: http://en.wikipedia.org/wiki/List_of_trigonometric_identities

Particulary the formulas for (cos theta cos phi) and (cos theta sin phi).
Combine these with the standard (cos^2 + sin^2) = 1.

 

[craig16]

Yaaa, i figured it out.

Just multiplying both sides of the r function by r, then subbing in y=rsin(theta) and x=rcos(theta) then using sin^2 + cos^2 =1 will make it just in terms of x and y.

 

[I like Serena]

Yaaa, i figured it out.

Just multiplying both sides of the r function by r, then subbing in y=rsin(theta) and x=rcos(theta) then using sin^2 + cos^2 =1 will make it just in terms of x and y.

So what did you end up with?
And do you have a geometric interpretation?