11-1

This week in Advanced Math, we covered all of Chapter 11. The whole Chapter consisted of formulas and was pretty simple. In 11-1, we were taught two conversion formulas – polar and rectangular.

x= r cos theta
y = r sin theta
(r, theta)
^ Used to convert to rectangular.

r = square root x^2 + y^2
tan theta = y/x
(x,y)
^Used to convert to polar

EXAMPLE 1: Give the polar coordinates for point (-3, 4).
1. Since we are converting to polar, use the red formulas.
2. r = square root of -3^2 + 4^2
3. r = +/- 5
4. Plug x and y into the tan function – 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 blue 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)