Solving a Polar Equation with Negative Numerator: Is It Possible?

  • Thread starter Thread starter merced
  • Start date Start date
  • Tags Tags
    Negative Polar
Click For Summary
SUMMARY

The discussion centers on the polar equation r = 5/(-1 + 2 cos θ) and the implications of having a negative numerator. The user transforms the equation to r = -5/(1 - 2 cos θ) to explore its validity. It is established that while the numerator (ed) is typically positive, a negative r value indicates a direction reversal in polar coordinates, allowing for valid graphing of the equation. The conclusion confirms that negative r values are permissible in polar equations.

PREREQUISITES
  • Understanding of polar coordinates and their graphical representation
  • Familiarity with trigonometric functions, specifically cosine
  • Knowledge of the standard form of polar equations r = ed/(1 + e cos θ)
  • Basic graphing skills in polar coordinates
NEXT STEPS
  • Research the properties of polar equations with negative r values
  • Learn about the implications of transformations in polar coordinates
  • Explore graphing techniques for polar equations using software like Desmos
  • Study the relationship between polar and Cartesian coordinates
USEFUL FOR

Mathematicians, students studying polar coordinates, and educators looking to enhance their understanding of polar equations and their graphical interpretations.

merced
Messages
44
Reaction score
1
I have the given polar equation that I have to graph.

r = 5/(-1 + 2 cos θ)

The format is r = ed/(1 +e cosθ)

(e and d are always positive)

I can solve multiply r by -1/-1 --> r = -5/(1 - 2 cosθ).

Is this possible? I thought that the numerator (ed) cannot be a negative number. Is this a misprint or is there a way to solve this?
 
Physics news on Phys.org
r can be negative... it just means that you actually go 180 degrees the other direction. So for example, when theta is 180 degrees, r is -5/3... so the point is at 5/3 on the *positive* x-axis.
 

Similar threads

Double Integral of function in region bounded by two circles
  • · Replies 19 ·
Replies
19
Views
3K
Show proof of point C in the given problem that involves Polar equation
  • · Replies 3 ·
Replies
3
Views
1K
Why is the Jacobian for polar coordinates sometimes negative?
  • · Replies 5 ·
Replies
5
Views
2K
Polar coordinates of the centroid of a uniform sector
  • · Replies 5 ·
Replies
5
Views
2K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
  • · Replies 1 ·
Replies
1
Views
2K
Reduction of order for Second Order Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Convert the Cartesian equation to the polar equation
  • · Replies 1 ·
Replies
1
Views
2K
Find the slope of the tangent at the given angle theta
  • · Replies 1 ·
Replies
1
Views
2K
Finding Polar Form Expressions: -3-3i & 2√3-2i
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Calculate the Tangent Line and Area for a Polar Curve?
  • · Replies 3 ·
Replies
3
Views
2K