Chapter 13-3: Intersections of Polar Curves
Ok, it's a nice and easy 2 page lesson. A break for all you lucky juniors and seniors in time for prom.
This lesson is discusses the basics on finding the intersections points when given two polar curves.
Basically to find the number of intersections, and the point they intersect, we insert the equation into the regular function mode. After that, we just do the regular calc -> intersect stuff...
For those that do not understand what I am saying...
I'll point out the different steps
1) Get out your calculator
2) Press Mode
3) Select Func if it is not already selected. (If you realized that Func stands for function, then you are really smart. =])
4) Press Y=
5) Insert equations!!!
6) Go to Window and set Xmin = 0 and Xmax =360 (this is because the polar coordinate system is 360 degrees.) The Ymin and max vary depending on the graph
7) Now, press graph!
8) OMG, a graph. Now we can not only find the number of times the two graphs intersect each other, but we can also find out WHERE they intersect each other.
9) I'm not going to explain the intersect stuff...we did it a million times already.
Ok, now that we have the intersection point...
The X-Coordinate is the degree, and the y is the r...
so the format will be (r, theta)
Alright...now to put all of this information into use...
We are given 2 equations, and we are required to find the intersection points between the two graphs.
Now, we graph them on our calculator. In polar mode, the two equations should look like this...
Ok...Now that we see the equations in Polar mode, now we switch to function mode. (For those who don't know how to do this...scroll up.)
Alright, now insert the equations the EXACT same way into y=
The resulting graph should look something like this.
Awesome...right? Now we use the Calc-> intersect powers of our calculator and find the intersections between the two graphs.
The resulting answers should be...
(117.531, -.387) (193.264, -1.919) (235.510, -.699) (287.063, 1.880)
Now, we have to change them into polar coordinates. Which is NOT that difficult guys.
All we have to do is swap them around and add a degree symbol to the x-coordinate...
(-.387, 117.531°) (-1.919, 193.264°) (-.699, 235.510°) (1.880, 287.063°)
Hurray! We solved the problem!!!
Since there I can't find a website truly discussing the intersections of Polar Curves...I'll post one up about some of the things we already learned for last lesson. Besides, this lesson was the easiest one we have had in a long time.
********** Katie You're Up Next. ***********
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