Rewrite polar equation as Cartesian (trig identities)

  • Thread starter craig16
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  • #1
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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 alot of rearranging, can't figure it out.
 

Answers and Replies

  • #2
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I'm not sure I understand. Are you trying to write [tex]\theta\ [/tex] and a in terms of x and y?

If so, take a look at x/y or y/x.
 
  • #3
I like Serena
Homework Helper
6,577
176

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.
 
  • #4
21
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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.
 
  • #5
I like Serena
Homework Helper
6,577
176
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?
 

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