Areas and Lengths in Polar Coordinates. Calculus 3

[salazar888]

Homework Statement

"Find the area of the region that lies inside both curves (as an example), r=((sqrt(3)) cos(theta)) , r=sin(theta). This is Calculus 3. Areas and lengths in polar coordinates.

Homework Equations

Guys, I'm very confused because when the polar graphs are complicated we obviously can use the calculator, but I'm having a lot of trouble finding my intersection points on my Texas TI-84 Plus. I have it on polar mode and it doesn't allow you to find intersection points but only to find "values" which is not hard when two polar curves are together, but does require you time during the test while you guess values for pi. My professor, unfortunately doesn't know what she is doing, she makes typos in class all the time and I'm tired of pointing them out. I honestly don't like using my calculator for this type of questions since you can just set up the two given curves equal to each other in order to find the points at which they intersect, but we know that sometimes in polar coordinate graphs you aren't able to find all your points algebraically unless you are very ingenious. So can anybody teach me how to rapidly find the intersection points of two polar curves using a TI-84 Plus.

The Attempt at a Solution

I try to trace but the values for theta are given in decimal form.

 

[lanedance]

why not solve for them analytically?

they will be where
\sqrt{3} cos(\theta) = sin(\theta)
\sqrt{3} = \frac{sin(\theta)}{cos(\theta)}