Question

The point $\left(5, \frac{\pi}{6}\right)$ can also be represented by which of the following polar coordinates? (a) $\left(5,-\frac{\pi}{6}\right)$ (b) $\left(-5, \frac{13 \pi}{6}\right)$ (c) $\left(5,-\frac{5 \pi}{6}\right)$ (d) $\left(-5, \frac{7 \pi}{6}\right)$

Name: Problem 8, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-17T04:17:36-08:00
Duration: 1 min 10 s
Channel: Katelyn Chen
Description: The point (5, (π)/(6)) can also be represented by which of the following polar coordinates? (a) (5,-(π)/(6)) (b) (-5, (13 π)/(6)) (c) (5,-(5 π)/(6)) (d) (-5, (7 π)/(6))

   The point $\left(5, \frac{\pi}{6}\right)$ can also be represented by which of the following polar coordinates?
(a) $\left(5,-\frac{\pi}{6}\right)$
(b) $\left(-5, \frac{13 \pi}{6}\right)$
(c) $\left(5,-\frac{5 \pi}{6}\right)$
(d) $\left(-5, \frac{7 \pi}{6}\right)$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 8

Instant Answer

Solved by Expert Katelyn Chen

06/17/2020

Step 1

In polar coordinates, the first value is the radius $r$ and the second value is the angle $\theta$. Show more…

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The point $\left(5, \frac{\pi}{6}\right)$ can also be represented by which of the following polar coordinates? (a) $\left(5,-\frac{\pi}{6}\right)$ (b) $\left(-5, \frac{13 \pi}{6}\right)$ (c) $\left(5,-\frac{5 \pi}{6}\right)$ (d) $\left(-5, \frac{7 \pi}{6}\right)$

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Key Concepts

Angle Equivalence

In polar coordinates, angles that differ by multiples of 2? represent the same direction. This means that adding or subtracting 2? (or any integer multiple thereof) to the angle does not change the location of the point, allowing for multiple equivalent representations.

Negative Radius

A negative radius in polar coordinates indicates a point located in the direction directly opposite to the one given by the specified angle. For a negative radius, the corresponding angle can be adjusted by adding ? (or 180°) to find an equivalent representation with a positive radius. This conversion allows for further flexibility in expressing the same point.

Polar Coordinates

Polar coordinates represent points in the plane using a distance from a fixed origin and an angle from a fixed direction. They are an alternative to Cartesian coordinates and are particularly useful in contexts where circular or rotational symmetry is present.

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