# Rectangular to Polar Conversion

• steveFerrera
In summary: You can simplify this even more by multiplying both sides by the cosine of theta: (r*cos(θ))*cos(θ) = r*cos2(θ)
steveFerrera

## Homework Statement

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

## 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!

## The Attempt at a Solution

Last edited:
steveFerrera said:

## 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?

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.)

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?

Last edited:
steveFerrera said:
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.
(am)n = am*n , not am+n.​

Is there a standard form it needs to be in?

Should i try an simplify it further?

Last edited:
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?

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.

## 1. What is the purpose of converting from rectangular to polar coordinates?

The purpose of converting from rectangular to polar coordinates is to represent a point in a two-dimensional plane using polar coordinates, which consist of a distance (r) from the origin and an angle (θ) from the positive x-axis. This representation can be useful in many applications, such as in physics, engineering, and mathematics.

## 2. How do you perform the conversion from rectangular to polar coordinates?

To convert from rectangular to polar coordinates, you can use the following formulas:

r = √(x² + y²)

θ = arctan(y/x)

where x and y are the rectangular coordinates of the point and r and θ are the polar coordinates. It is important to note that the angle (θ) is measured in radians, not degrees.

## 3. What is the relationship between rectangular and polar coordinates?

The relationship between rectangular and polar coordinates is that they both represent the same point in a two-dimensional plane. Rectangular coordinates use the x and y axes to indicate the position of a point, while polar coordinates use the distance from the origin and the angle from the positive x-axis to represent the point.

## 4. What are the advantages of using polar coordinates over rectangular coordinates?

One of the main advantages of using polar coordinates over rectangular coordinates is that they are often more convenient and efficient for representing points in circular or radial patterns. This is because the distance (r) and angle (θ) in polar coordinates can easily describe a point's position in relation to the origin, whereas rectangular coordinates may require more complex calculations.

## 5. Can you convert from polar to rectangular coordinates?

Yes, you can convert from polar to rectangular coordinates using the following formulas:

x = r * cos(θ)

y = r * sin(θ)

where x and y are the rectangular coordinates and r and θ are the polar coordinates. This conversion can be useful when you need to plot points in a rectangular coordinate system or perform calculations that require rectangular coordinates.

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