Polar Coordinate System - Video Tutorials & Practice Problems
Intro to Polar Coordinates
Video transcript
Intro to Polar Coordinates Example 1
Video transcript
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,−611π)
Plot the point on the polar coordinate system.
(−2,32π)
Determining Different Coordinates for the Same Point
Video transcript
Plot the point (3,2π) & 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.
(3,25π),(−3,−23π),(−3,23π)
(3,25π),(3,−23π),(−3,23π)
(−3,25π),(−3,−23π),(−3,2π)
(3,25π),(3,−23π),(−3,2π)
Determining Different Coordinates for the Same Point Example 2
Video transcript
Plot the point (5,−3π), then identify which of the following sets of coordinates is the same point.
(−5,−3π)
(−5,3π)
(−5,32π)
(−5,35π)
Plot the point (−3,−6π), then identify which of the following sets of coordinates is the same point.
(−3,611π)
(−3,65π)
(3,611π)
(3,6π)
Do you want more practice?
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 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 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on t...
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point wit...
- Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of θ.
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point wit...
- 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
- In Exercises 11–20, 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 − sin θ
- In Exercises 11–20, 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 = 2 + 2 cos θ
- In Exercises 11–20, 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 = 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
- In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point wit...
- In Exercises 27–32, select the representations that do not change the location of the given point. (7, 140°) ...
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 4 sin 3θ
- In Exercises 27–32, select the representations that do not change the location of the given point. (4, 120°) ...
- In Exercises 27–32, select the representations that do not change the location of the given point. (2, − 3π/4...
- In Exercises 27–32, select the representations that do not change the location of the given point. (−2, 7π/6)...
- In Exercises 27–32, select the representations that do not change the location of the given point. (−5, − π/4...
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − 3 sin θ
- In Exercises 27–32, select the representations that do not change the location of the given point. (−6, 3π) ...
- In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (...
- In Exercises 13–34, test for symmetry and then graph each polar equation. r cos θ = −3
- In Exercises 35–44, test for symmetry and then graph each polar equation. r = cos θ/2
- In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (...
- In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (...
- In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Ex...
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Ex...
- In Exercises 35–44, test for symmetry and then graph each polar equation. r = 2 + 3 sin 2θ
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Ex...
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Ex...
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. 3x ...
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x =...
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x² ...
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. (x ...
- In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rect...
- In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rect...
- In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate s...
- In Exercises 61–63, test for symmetry with respect to a. the polar axis. b. the line θ = π/2. c. the...
- In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate s...
- In Exercises 64–70, graph each polar equation. Be sure to test for symmetry. r = 2 + 2 sin θ
- In Exercises 64–70, graph each polar equation. Be sure to test for symmetry. r = 2 + cos θ
- In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate s...
- In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate s...
- In Exercises 79–80, convert each polar equation to a rectangular equation. Then determine the graph's slope an...
- In Exercises 81–82, find the rectangular coordinates of each pair of points. Then find the distance, in simpli...
- In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangul...
- In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangul...
- In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangul...
- In calculus, it can be shown that e^(iθ) = cos θ + i sin θ. In Exercises 87–90, use this result to plot ea...
- In calculus, it can be shown that e^(iθ) = cos θ + i sin θ. In Exercises 87–90, use this result to plot ea...