# Polar Coordinate System - Video Tutorials & Practice Problems

## Intro to Polar Coordinates

## Intro to Polar Coordinates Example 1

Plot the point on the polar coordinate system.

$(5,210°)$

Plot the point on the polar coordinate system.

$(-3,-90°)$

Plot the point on the polar coordinate system.

$(6,-\frac{11\pi}{6})$

Plot the point on the polar coordinate system.

$(-2,\frac{2\pi}{3})$

## Determining Different Coordinates for the Same Point

Plot the point $(3,\frac{\pi}{2})$ & find another set of coordinates, $(r,θ)$, for this point, where:

(A) $r≥0,2π≤θ≤4π$,

(B) $r≥0,-2π≤θ≤0$,

(C) $r≤0,0≤θ≤2π$.

$(3,\frac{5\pi}{2}),(-3,-\frac{3\pi}{2}),(-3,\frac{3\pi}{2})$

$(3,\frac{5\pi}{2}),(3,-\frac{3\pi}{2}),(-3,\frac{3\pi}{2})$

$(-3,\frac{5\pi}{2}),(-3,-\frac{3\pi}{2}),(-3,\frac{\pi}{2})$

$(3,\frac{5\pi}{2}),(3,-\frac{3\pi}{2}),(-3,\frac{\pi}{2})$

## Determining Different Coordinates for the Same Point Example 2

Plot the point $(5,-\frac{\pi}{3})$, then identify which of the following sets of coordinates is the same point.

$(-5,-\frac{\pi}{3})$

$(-5,\frac{\pi}{3})$

$(-5,\frac{2\pi}{3})$

$(-5,\frac{5\pi}{3})$

Plot the point $(-3,-\frac{\pi}{6})$, then identify which of the following sets of coordinates is the same point.

$(-3,\frac{11\pi}{6})$

$(-3,\frac{5\pi}{6})$

$\left(3,\frac{11\pi}{6}\right)$

$(3,\frac{\pi}{6})$

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### Your Trigonometry tutors

- In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on t...
- In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on t...
- In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on t...
- In Exercises 7–12, test for symmetry with respect to a. the polar axis. b. the line θ=π2. c. the pol...
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point wit...
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- In Exercises 13–14, graph each polar equation. r = 1 + sin θ
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 cos θ
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- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − sin θ
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 + 2 cos θ
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 + cos θ
- In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point wit...
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 + 2 cos θ
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 − 3 sin θ
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- In Exercises 27–32, select the representations that do not change the location of the given point. (7, 140°) ...
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- In Exercises 64–70, graph each polar equation. Be sure to test for symmetry. r = 2 + 2 sin θ
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