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The basics of polar coordinates, including the concept of a polar axis, the pole, and the representation of points using r and theta. It also covers the sign of r, multiple representations of points, and the relations between polar and rectangular coordinates. Additionally, it provides examples of finding polar and rectangular coordinates.
What you will learn
Typology: Lecture notes
Uploaded on 09/12/2022
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The foundation of the polar coordinate system is a horizontal ray that extends to the right.
The ray is called the polar axis.
The endpoint of the ray is called the pole.
The point 𝑃 = 𝑟, 𝜃 is located 𝑟 units from the pole. -- 𝑟 > 0, the point lies along the terminal n side of 𝜃. -- 𝑟 < 0, the point lies along the ray opposite the terminal side of 𝜃. -- 𝑟 = 0, the point lies at the pole, regardless of 𝜃.
Plot the point.
Plot the point.
If n is any integer, the point (𝑟, 𝜃) can be represented as
𝑟, 𝜃 = (𝑟, 𝜃 + 2𝑛𝜋) or
Find 3 representations
(5,
𝜋 4 )
a. r is positive and 2𝜋 < 𝜃 < 4𝜋
b. r is negative and 0 < 𝜃 < 2𝜋
c. r is positive and −2𝜋 < 𝜃 < 0
Graph of a Circle
r 𝑠𝑖𝑛𝜃 = y 𝑐𝑜𝑠𝜃 = θ 𝑡𝑎𝑛𝜃 = x 𝑥 = 𝑦 = 𝑡𝑎𝑛𝜃 =
Not on Unit Circle
Find the Polar Coordinates
Find the Polar Coordinates