[Not Homework] Polar Equation Problem Involved Tangents

In summary, a polar equation is a mathematical expression that relates a point in the polar coordinate system to its distance from the origin and angle from the polar axis. To graph a polar equation, substitute different values for the angle and connect the points with a smooth curve. Tangents in polar equations are lines that touch the curve at a single point and are perpendicular to the radius vector at that point. The point of tangency can be found by using the derivative of the equation and setting it equal to zero. Some polar equations can have multiple tangents, known as points of inflection, which can be found by taking the second derivative and setting it equal to zero.
  • #1
suporia
3
0
Not homework, just trying to learn how to solve this problem for an exam.

Homework Statement



https://dl.dropbox.com/u/23889576/Screenshots/10.png

Homework Equations



[itex]\int_{a}^{b} \sqrt { (\frac{dr}{dθ})^2 + r^2 }\, dθ[/itex]

The Attempt at a Solution



Had much difficulty, could not even derive the original derivative function for this problem.
 
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  • #2
welcome to pf!

hi suporia! welcome to pf! :wink:

the figure is symmetric, so when one bug is at (r,θ), the next is at (r,θ+π/2) …

does that help? :smile:
 

Related to [Not Homework] Polar Equation Problem Involved Tangents

1. What is a polar equation?

A polar equation is a mathematical expression that relates a point in the polar coordinate system to its distance from the origin and its angle from the polar axis.

2. How do I graph a polar equation?

To graph a polar equation, plot points by substituting different values for the angle and then connecting the points with a smooth curve. You can also use a graphing calculator or online graphing tool to plot the equation.

3. What are tangents in polar equations?

In polar equations, tangents are lines that touch the curve at a single point and are perpendicular to the radius vector at that point. They indicate the direction in which the curve is changing at that point.

4. How do I find the point of tangency in a polar equation?

To find the point of tangency in a polar equation, you can use the derivative of the equation and set it equal to zero. Then solve for the angle value that makes the derivative equal to zero, and plug that angle into the polar equation to find the corresponding point.

5. Can polar equations involve multiple tangents?

Yes, some polar equations can have multiple tangents at different points on the curve. These are called points of inflection and occur when the curve changes direction at that point. To find points of inflection, you can take the second derivative of the equation and set it equal to zero.

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