Convert another equation x^2+y^2=4 to polar form

Click For Summary

Discussion Overview

The discussion revolves around converting the Cartesian equation \(x^2+y^2=4\) into polar form. Participants explore the mathematical steps involved in this conversion, focusing on the application of trigonometric identities and the implications of the resulting polar equation.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant begins with the equation \(x^2+y^2=4\) and expresses uncertainty about the next steps after rewriting it in terms of polar coordinates.
  • Another participant suggests squaring the trigonometric functions and provides the transformation to polar coordinates, leading to the equation \(r^2\cos^2(\theta)+r^2\sin^2(\theta)=4\).
  • A similar response reiterates the need to apply trigonometric identities after factoring the left-hand side of the equation.
  • A later reply confirms understanding and notes that the polar form represents a circle centered at the origin, indicating that the polar equation simplifies to \(r=a\) for a constant \(a\).

Areas of Agreement / Disagreement

Participants generally agree on the steps to convert the equation and the interpretation of the resulting polar form, though the discussion does not explicitly resolve all uncertainties regarding the application of trigonometric identities.

Contextual Notes

Some assumptions about the application of trigonometric identities and the implications of the polar form remain unaddressed, particularly regarding the generalization of the polar equation for different values of \(a\).

Elissa89
Messages
52
Reaction score
0
x^2+y^2=4

I have so far:

(r^2)cos^(theta)+(r^2)sin(theta)=4

Idk what I'm supposed to do from here
 
Mathematics news on Phys.org
You need to also square the trig. functions:

$$x^2+y^2=4$$

$$(r\cos(\theta))^2+(r\sin(\theta))^2=4$$

$$r^2\cos^2(\theta)+r^2\sin^2(\theta)=4$$

Factor the LHS...what do you have...is there a trig. identity you can apply?
 
MarkFL said:
You need to also square the trig. functions:

$$x^2+y^2=4$$

$$(r\cos(\theta))^2+(r\sin(\theta))^2=4$$

$$r^2\cos^2(\theta)+r^2\sin^2(\theta)=4$$

Factor the LHS...what do you have...is there a trig. identity you can apply?

got it! thanks!
 
Elissa89 said:
got it! thanks!

We see we have a circle centered at the origin, and in polar coordinates, that's simply a constant value for \(r\). The Cartesian equation:

$$x^2+y^2=a^2$$ where \(0<a\)

Has the polar equation:

$$r=a$$
 

Similar threads

Graduate Converting this vector into polar form
  • · Replies 4 ·
Replies
4
Views
2K
High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
2K
MHB Convert equation 8x=8y to polar form
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Plotting polar equations and scale invariance
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K
MHB Convert r=7cos(theta) into a rectangular equation
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Cartesian to Polar form.... Is it just a transformation of the plane?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
MHB -11.7.94 Find the rectangular equation
  • · Replies 2 ·
Replies
2
Views
1K
MHB What are the coordinates of points equidistant from (1,0) and (5,4)?
  • · Replies 6 ·
Replies
6
Views
1K