Finding Points of Intersection for Polar Curves

In summary, the conversation is discussing how to find the two points of intersection in polar form for two given curves. The first approach involves setting the curves equal to each other and simplifying. The second approach involves using the trigonometric identity tanθ=sinθ/cosθ and solving for θ. The person mentions using θ=π/4 to find one of the points, but it is unclear how they arrived at this answer. The other person suggests finding the second point using a different value of θ where tan(θ) = 1 and considering the period of the tangent function.
  • #1
jjeddy
3
0

Homework Statement


I need to find the 2 points of intersection (in polar form) of the two curves.

I know just by looking that the origin will be one of the points, (0,0)

The Attempt at a Solution



I have approached this two different ways,

1. set them equal to each other and tried to simplify.Which approach should i use?
 
Last edited:
Physics news on Phys.org
  • #2
OK, i used tanθ=sinθ/cosθ and i solved for θ

i can substitute back into get my corresponding (r,θ) r point and i should have my point right?
 
Last edited:
  • #3
Right. That gives you one of the points. I'm not quite sure how you came up with your answer of θ=π/4 , so it's difficult to suggest how you should come up with the second point.
 
  • #4
Is that right?I think that is my polar coordinate where it intersects
 
Last edited:
  • #5
Your first post states that you need to find the 2 points of intersection.

For what other value of θ, is tan(θ) = 1 ? What is the period of the tangent function?
 

1. What are points of intersection?

Points of intersection are points where two or more lines or curves cross each other. In other words, they are the locations where the graphs of two or more equations overlap.

2. How do you find points of intersection?

To find points of intersection, you can use algebraic methods by solving the equations simultaneously. This can be done by substitution, elimination, or graphing. Alternatively, you can also use graphical methods by visually identifying where the lines or curves intersect on a graph.

3. Can there be more than one point of intersection?

Yes, there can be more than one point of intersection between two or more lines or curves. The number of points of intersection depends on the number of equations and their relationship with each other. For example, two non-parallel lines can intersect at one point, while two parabolas can intersect at two points.

4. What does the point of intersection represent?

The point of intersection represents the coordinates where the two or more lines or curves meet. This point is a solution to all the equations involved and can have real or imaginary values.

5. Why are points of intersection important in mathematics and science?

Points of intersection are important in mathematics and science because they allow us to solve and understand systems of equations and their relationships. They can also represent real-life situations, such as the intersection of two paths or the intersection of supply and demand curves in economics.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
680
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
22
Views
1K
  • Calculus and Beyond Homework Help
Replies
15
Views
2K
  • Calculus and Beyond Homework Help
Replies
16
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
829
Back
Top