Polar graphs really important and tangents

In summary, The conversation discusses finding points on a cardioid where the tangents are perpendicular to the initial line. The solution provided does not include pi because the equation used is dx/dy=0, which is equivalent to dx/dθ=0 except for θ=π.
  • #1
phospho
251
0
Hi, I really need help with this as exam is tomorrow

The question is to find the points on the cardioid r=a(1+costheta) where the tangents are perpendicular to the initial line

here is the answer

http://gyazo.com/e8b4cbd36f0ef71d0cdf13be256d8618

Why is pi not included in the solution, while if I was finding parallel to the initial line then pi would be included.

please help
 
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  • #2
hi phospho! :smile:
phospho said:
Why is pi not included in the solution, while if I was finding parallel to the initial line then pi would be included.

you're solving dx/dθ = 0

but you're using an x,y graph, so you really need to solve dx/dy = 0

ie dx/dθ / dy/dθ = 0

the solutions to this are the same as the solutions to dx/dθ = 0, except if dy/dθ = 0 (which it is for θ = π) :wink:
 

1. What is a polar graph and why is it important in science?

A polar graph is a type of graph that represents data using polar coordinates, with the angle and distance from the origin being the variables. It is important in science because it allows for the visualization and analysis of data that is circular or has a directional component, such as in biology, physics, and engineering.

2. How are polar graphs used in scientific research?

Polar graphs are commonly used in scientific research to plot and analyze data from experiments, simulations, and observations. They can show relationships between variables, patterns, and trends that may not be easily seen in traditional Cartesian graphs.

3. Can polar graphs be used to represent tangents?

Yes, polar graphs can be used to represent tangents, which are lines that touch a curve at only one point and have the same slope as the curve at that point. In polar coordinates, tangents are represented by lines that are perpendicular to the radius vector at the point of tangency.

4. What is the relationship between polar graphs and tangents?

The relationship between polar graphs and tangents is that the tangent lines on a polar graph represent the instantaneous slope of the curve at a particular point. This can be useful in determining the direction and rate of change of a variable in relation to another.

5. Can polar graphs and tangents be used in real-world applications?

Yes, polar graphs and tangents have many real-world applications, such as in navigation, astronomy, and mapping. They can also be used in analyzing and optimizing curves and shapes in engineering and design. Additionally, polar graphs are often used in computer graphics and animation to create smooth and realistic movements.

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