Given the point with polar coordinates , which of the following polar coordinate pairs labels the same point?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 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
Multiple Choice
Given the polar equation , which of the following is the corresponding Cartesian equation?
A
B
C
D
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Verified step by step guidance1
Recall the relationship between polar and Cartesian coordinates: \(x = r \cos \theta\) and \(y = r \sin \theta\).
Given the polar equation \(r = 6\), this means the distance from the origin to any point on the curve is always 6.
To convert to Cartesian form, use the identity \(r^2 = x^2 + y^2\) which relates the radius in polar coordinates to \(x\) and \(y\) in Cartesian coordinates.
Substitute \(r = 6\) into the identity to get \$6^2 = x^2 + y^2$.
Simplify the equation to \(x^2 + y^2 = 36\), which is the Cartesian equation of a circle with radius 6 centered at the origin.
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