Chapter 11- Section 1

This week in Advanced Math, we were introduced to Chapter 11. To be honest i feel this chapter is quite simple. Calculators are still forbidden of use on test but we were allowed to use them for homework. These chapters all feed off of one another, and are accumlative. In 11-1, we were taught two conversion formulas – polar and rectangular.

x= r cos theta and y = r sin theta (formulas used to convert to Rectangular form)
r = square root x^2 + y^2 and tan theta = y/x (formulas used to convert to Polar form)

Points will be given to you like this:

(x , y ) <----Rectangular

(r, theta) <------Polar

EXAMPLE 1: Give the polar coordinates for point (-3, 4).

1. Since we are converting to polar, use the pink formulas.
2. r = square root of -3^2 + 4^2
3. r = +/- 5
4. (Plug x and y into the tan function y/x) tan theta = 4/-3
5. Since tan is negative, find the angles in quadrants 2 and 4 – 126.87 degrees and 306.87 degrees
6. Since the angles are negative, +5 will get the bigger angle.
7. Your answer is (5, 306.87 degrees) and (-5, 126.87 degrees)

EXAMPLE 2: Convert (3, pi/2) to rectangular.
1. Since we are converting to rectangular, use the green formulas.
2. x = 3 cos pi/2 and y = 3 sin pi/2
3. Pi/2 is in your trig chart so continue simplifying.
4. x = 3(0) and y = 3(1)
5. Your answer is (0,3)