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how does r=2cos3(theta) = r=2cos(theta)(cos(theta)^2-(3 sin(theta)^2)) in polar equations terms

 Jun 21, 2015

Best Answer 

 #4
avatar+27558 
+10

Polar and Cartesian:

.

 Jun 21, 2015
 #1
avatar+99361 
+5

I only just noticed "in polar form" so I am not sure what you need.   

 

I can certainly show that they are the same.

You are actually asking me to show that

 

$$\\2cos3\theta=2cos\theta( Cos^2\theta-3sin^2\theta)\\\\
LHS=2cos3\theta\\\\
LHS=2[cos2\theta cos\theta-sin2\theta sin\theta]\\\\
LHS=2[(cos^2\theta-sin^2\theta) cos\theta-(2sin\theta cos\theta sin\theta)]\\\\
LHS=2cos\theta [cos^2\theta -sin^2\theta -2sin^2\theta ]\\\\
LHS=2cos\theta( Cos^2\theta-3sin^2\theta)\\\\
LHS=RHS$$

.
 Jun 21, 2015
 #2
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+5

Thanks i think that should work i just have an investigation on Polar equations and the question was show how r=2cos3(theta) is euqal to ^2=2x^3-6xy^2

 

Knowing that (x^2+y^2)=r^2

x=rcos(theta)

y=rsin(theta)

 Jun 21, 2015
 #3
avatar+99361 
0

Yes, that is right     

 

But I still don't know how the answer should be set out :/

 Jun 21, 2015
 #4
avatar+27558 
+10
Best Answer

Polar and Cartesian:

.

Alan Jun 21, 2015
 #5
avatar+99361 
0

Thanks Alan,

 

So then you just have to show that the other equation is the same ? (Which is easy to do)

So you need to work on both equations and get to the same polar equation.  :/     

---------------------------

I am still confused though.  I understand the algebra, no problems, but I don't understand how it all goes together.  

I am not explaining well because I am not quite sure what it is that I don't understand.  

I just know that there is something that I don't quite get here.  

Maybe a graph would help?        

 Jun 21, 2015

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