How to graph polar equations

In summary, the speaker is a junior in high school taking Calculus BC and Physics B and is currently learning about polar equations. They are having trouble understanding the concept and one of the questions they received is how to find the area of an equation excluding the overlapping part without using a calculator. The speaker also mentions they are unsure how to use the "tex" thing. They are given a formula and a hint for solving the problem.
  • #1
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It's my first time here so I guess I have to introduce myself first.

I am a junior in high school taking Calculus BC and Physics B (taking Physics C next year).
Currently, as of September 29, 2008, my class is learning of Polar equations.

We just went over basics but I am not perfectly grasping the concept on using polars.

One of the question I received during class was:

r=1/2 + sin([tex]\theta[/tex]

Now, without using calculator, how do I find the area of the equation which excludes the overlaping part.

I know that

A=1/2[tex]\int[/tex]r^2 d[tex]\theta[/tex]
but here we would subtract the inner area.
No point in using calculator;;; I cannot check my answer either since my teacher said the right answer choice is not shown (it is a multiple choice question).

ps. I don't know how to use the "tex" thing so...
 
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  • #2
jun9008 said:
It's my first time here so I guess I have to introduce myself first.

I am a junior in high school taking Calculus BC and Physics B (taking Physics C next year).
Currently, as of September 29, 2008, my class is learning of Polar equations.

We just went over basics but I am not perfectly grasping the concept on using polars.

One of the question I received during class was:

r=1/2 + sin([tex]\theta[/tex]

Now, without using calculator, how do I find the area of the equation which excludes the overlaping part.

I know that

A=1/2[tex]\int[/tex]r^2 d[tex]\theta[/tex]
but here we would subtract the inner area.
No point in using calculator;;; I cannot check my answer either since my teacher said the right answer choice is not shown (it is a multiple choice question).

ps. I don't know how to use the "tex" thing so...
Well, what have you done? You have given the formula. What do you get when you do the integration? One thing you can do is a quick graph of the region to see what "overlapping" part they are talking about. It's not that difficult even without a calculator! But I'll give you a hint: for [itex]\theta[/itex]= 0 to [itex]\pi[/itex], the graph looks about like an ellipse. For [itex]\theta= \pi[/itex] to [itex]2\pi[/itex], it is a smaller ellipse inside the first one.
 

1. How do I convert a Cartesian equation to a polar equation?

To convert a Cartesian equation to a polar equation, you can use the following formulas:
x = rcosθ
y = rsinθ
where r is the distance from the origin to the point, and θ is the angle formed by the point with the positive x-axis. Simply substitute these equations into the original Cartesian equation to get the polar equation.

2. How do I graph a polar equation?

To graph a polar equation, first plot points by substituting different values of θ into the equation and calculating the corresponding r value. Then, connect these points to create a continuous curve. It may also be helpful to use a graphing calculator or online graphing tool.

3. How do I determine the symmetry of a polar graph?

A polar graph can have either symmetry about the origin, the x-axis, or the y-axis. To determine the symmetry, replace θ with -θ in the equation and simplify. If the resulting equation is the same, the graph has symmetry about the origin. If the sign of the r value changes, the graph has symmetry about the x-axis. If the sign of θ changes, the graph has symmetry about the y-axis.

4. How do I find the intercepts of a polar graph?

To find the intercepts of a polar graph, set θ to 0 or π/2 (depending on the quadrant) and solve for r. This will give you the distance from the origin to the point where the graph intersects the x or y-axis.

5. How do I determine the domain and range of a polar equation?

The domain of a polar equation is all possible values of θ that would give a valid point on the graph. The range is all possible values of r for a given θ. To determine the domain, consider any restrictions on θ (such as a restricted interval) or any points where the graph is undefined. To determine the range, consider the behavior of the graph as θ approaches infinity.

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