11-1

This week in advanced math we started and finished chapter 11. Chapter 11 consist of three sections that deal with polar, complex numbers and De Moivre’s Theorem. Section 11-1 was the easiest so let’s review. All you need to know is how to convert to rectangular and polar.

Formulas:

Convert to Rectangular
x = r cos θ
y = r sin θ

Convert to Polar
r = square root x2 + y2
tan θ = y/x

Let’s try some example problems

Example 1:
Convert (4, 45°) to rectangular

x = 4 cos 45° = 4(square root 2/2) = 4
y = 4 sin 45° = 4(square root 2/2) = 4
Your answer (4,4)

Example 2:
Convert (2, π/3) to rectangular

x = 2 cos 60° = 2 (1/2) = 1
y = 2 sin 60° = 2 (square root 2/2) = square root 3
Your answer (1, square root 3)

Example 3:
Give the polar coordinates (6, 8)

1. r = square root 62 + 82
2. square root 100 = +/- 10
3. tan θ = 8/6 reduces to 4/3
4. θ = tan-1(4/3) = 53.130°
5. You want 2 answers so add 180 and get 233.130°