Module 8 Study Guide Page 1

Key Terms: 8.01

1. polar coordinate plane

2. pole

A. coordinate system where each point

may be represented by (

r

,

θ

), where

r

is the

directed distance from the pole and

θ

is the

directed angle from the polar axis

B. origin of the polar coordinate system

Points: Polar to Rectangular/Rectangular to Polar

Fill in the example:

Polar to Rectangular

Coordinate

(𝑟, θ) →(𝑥, 𝑦)

Rectangular to Polar

Coordinate

(𝑥, 𝑦) → (𝑟, θ)

Example: (5, π

6)

x-coordinate

𝑥 = 𝑟(𝑐𝑜𝑠 θ)

𝑟 = 𝑥2+𝑦2

y-coordinate

𝑦 = 𝑟(𝑠𝑖𝑛 θ)

θ = 𝑡𝑎𝑛−1(𝑦

𝑥)

x = 5(cosπ/6)

y = r(sinπ/6)

= 0.0456

= 5