Rectangular to Polar Conversion

[steveFerrera]

Homework Statement

I need to convert this to polar form; anyone have any ideas where to start?

Homework Equations

The Attempt at a Solution

I know this is incorrect but I am a bit overwelmed on this one.

any help would be wonderful! thanks!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

(x^2+y^2)^3=2x^2-2y^2

I need to convert this to polar form; anyone have any ideas where to start?

Homework Equations

r^2=x^2+y^2
y=r*sin(theta)
x=r*cos(theta)
tan(theta)=x/y

The Attempt at a Solution

(r^2)^3=2cos^2(theta)-2sin^2(theta)


I know this is incorrect but I'm a bit overwhelmed on this one.

any help would be wonderful! thanks!

You didn't include r when substituting for x & y on the right hand side of the equation.

Simplify (r²)³ by combining exponents. (Do this by using the properties of exponents.)

 

[steveFerrera]

did i do the substitutions right on the right side of the equation? or do i need to do some other manipulation of my relevant equations?

 

[SammyS]

r^5=2cos^2(theta)-2sin^2(theta)

did i do the substitutions right on the right side of the equation? or do i need to do some other manipulation of my relevant equations?

Regarding the right hand side:

If x = r*cos(θ), then what is x² ? Similar question for y.​

r⁵ is wrong too.

(a^m)ⁿ = a^m*n , not a^m+n.​

 

[steveFerrera]

Is there a standard form it needs to be in?

Should i try an simplify it further?

 

[Clever-Name]

There's another simple step to simplify it further. What can you factor out of the right hand side that might allow for some cancelling?

 

[SammyS]

On the right hand side you can do the squaring. For instance:

(r*cos(θ))² = r²*cos²(θ)​

A similar result holds for the other term. Then, factor out 2*r². Then, divide both sides by r². Then there is a double angle identity on the right side.