I have 11 problems to do--all relating to finding the domains of polar equations--a concept that I don't understand.
Here are the graphs of the equations whose domains I need to find. The dashed lines indicate where the graph is undefined. If you can do them all, awesome, but at least 3 or 4 examples should suffice. I've bolded the ones I think are the most important in case no one has time or doesn't want to do them all:
1. http://i265.photobucket.com/albums/i...olargraph3.jpg (General equation: r = 2cos2θ)
2.http://i265.photobucket.com/albums/i...olargraph4.jpg (General equation: r = 3sin2θ)
3. http://i265.photobucket.com/albums/i...olargraph5.jpg (General equation: r = 2cosθ)
4. http://i265.photobucket.com/albums/i...olargraph6.jpg (General equation: r = -2sinθ)
5. http://i265.photobucket.com/albums/i...olargraph7.jpg (General equation: r = -sin3θ)
6. http://i265.photobucket.com/albums/i...olargraph8.jpg (General equation: r = -sin3θ)
7. http://i265.photobucket.com/albums/i...olargraph9.jpg (General equation: r = -sin3θ)
8. http://i265.photobucket.com/albums/i...largraph10.jpg (General equation: r = -sin3θ yet again)
9. http://i265.photobucket.com/albums/i...largraph11.jpg (General equation: r = 3cos4θ--this one was deemed "super difficult" by my teacher)
Now you need to consider the ranges of and under the given rstrictions on .
I'll outline one way of doing this for (the method can be used for the other one):
Then which is a parabola.
By considering the restriction on you can get the restriction on and hence the restriction on a.
So sketch a graph of over the restricted values of a and use it to read off the range of values of x.
The spade work is left for you.
Your teacher obviously has a more elementary approach in mind. Not being able to see your class notes or textbook, I really can't tell what that might be. For all I know, your teacher wants you to spreadsheet the values of x and y. Or read them off from an accurately drawn curve. Or use a graphics calculator to draw the polar curves. Or convert to cartesian coordinates and plot points. Or graph and with a graphics calculator.
Does your teacher expect you to use technology? Because I don't see any way of avoiding trig identities if algebraic 'by-hand' solutions are required.
Perhaps someone else can make a suggestion.
Here's a thought - maybe you can provide some detailed information on what your background is and what you've actually done in this topic. Has your teacher done any similar examples in class? - if so, what method did s/he use.
There are usually several ways of solving a problem - but understanding them is totally dependent on ones mathematical background. Of course, I have no idea what your background is - have you studied trig identities (compound angle formulae, double angle formulae etc.)?