Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
9. Polar Equations
Polar Coordinate System
1:06 minutes
Problem 11a
Textbook Question
Textbook QuestionIn Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (2, 45°)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polar Coordinates
Polar coordinates represent points in a two-dimensional space using a distance from a reference point (the pole) and an angle from a reference direction (usually the positive x-axis). The format is (r, θ), where 'r' is the radial distance and 'θ' is the angle in degrees or radians. This system is particularly useful for representing circular or spiral patterns.
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Plotting Points in Polar Coordinates
To plot a point given in polar coordinates, first identify the radial distance 'r' and the angle 'θ'. From the pole, measure the angle 'θ' counterclockwise from the positive x-axis, then move outward from the pole a distance of 'r'. If 'r' is negative, move in the opposite direction along the line defined by the angle.
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Conversion Between Polar and Cartesian Coordinates
Understanding how to convert between polar and Cartesian coordinates is essential for interpreting polar points. The conversion formulas are x = r * cos(θ) and y = r * sin(θ). This allows you to translate polar coordinates into the familiar (x, y) format, facilitating easier plotting on a Cartesian grid.
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