11-1

This section is on polar and rectangular coordinates.
When you graph, you have to use (r, theta) instead of (x,y).

There are a couple of formulas you need to know for this section.
When you convert from polar to rectangular: x=rcostheta, y=rsintheta.
When you convert from rectangular to polar: r=square root of x^2+y^2, theta=tan^-1(y/x).

Example 1: Give the polar coordinate for (6,3)

1. First, you have to use the formulas I gave you above ^^^. R=square root of 6^2+3^2= square root of 36+9=square root of 45. Theta=tan^-1 (3/6)=tan^-1 (1/2)=26 degrees 33 minutes 54 seconds, 206 degrees 33 minutes 54 seconds.
2. Now you have to find out what quadrant the point (6,3) is in: It's in the first quadrant.
3. Since it is in the first quadrant, you now have to find out what answer from your theta would put you in the first quadrant: that would be 26 degrees 33 minutes 54 seconds.
4. Now you can have your final answer which is: (square root of 45, 26 degrees 33 minutes 54 seconds) and (-square root of 45, 206 degrees 33 minutes 54 seconds.

Example 2: Give the rectangular coordinates for (6, 30 degrees).

1. Giving the rectangular coordinates is easier than giving the polar coordinates and it is faster.
2. The first thing you need to know is that 6 is your R and 30 degrees is your Theta.
3. Now you use your formulas from above ^^^^^.
4. X=RcosTheta=6cos30 degrees=6(square root of 3/2)=6square root of 3/2=3 square root of 3.
5. Y=RsinTheta=6sin30 degrees=6(1/2)=6/2=3.
6. Final answer: (3 square root of 3, 3).

-Amber :)