For the point with polar coordinates (1,-(π)/(2)), which of the following best describes the loc

Name: Problem 7, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-17T04:15:44-08:00
Duration: 36 s
Channel: Katelyn Chen
Description: For the point with polar coordinates (1,-(π)/(2)), which of the following best describes the location of the point in a rectangular coordinate system? (a) in quadrant IV (b) on the y-axis (c) in quadrant II (d) on the x-axis

step 1 For this question, we're giving the polar coordinate 1 negative pi over 2. So we can think of th

Question

For the point with polar coordinates $\left(1,-\frac{\pi}{2}\right)$, which of the following best describes the location of the point in a rectangular coordinate system? (a) in quadrant IV (b) on the $y$-axis (c) in quadrant II (d) on the $x$-axis

   For the point with polar coordinates $\left(1,-\frac{\pi}{2}\right)$, which of the following best describes the location of the point in a rectangular coordinate system?
(a) in quadrant IV
(b) on the $y$-axis
(c) in quadrant II
(d) on the $x$-axis

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

Michael Sullivan 4th Edition

Chapter 8, Problem 7

Instant Answer

Solved by Expert Katelyn Chen

06/17/2020

Step 1

The point is given in polar coordinates as $(1, -\frac{\pi}{2})$, where $1$ is the radius $r$ and $-\frac{\pi}{2}$ is the angle $\theta$. Show more…

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For the point with polar coordinates $\left(1,-\frac{\pi}{2}\right)$, which of the following best describes the location of the point in a rectangular coordinate system? (a) in quadrant IV (b) on the $y$-axis (c) in quadrant II (d) on the $x$-axis

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Key Concepts

Understanding Axes and Quadrants

In the rectangular coordinate system, points located where one of the coordinates is zero lie on an axis. Recognizing that points with a zero x-coordinate or y-coordinate are on the y-axis or x-axis respectively is crucial when identifying the specific location of a point, such as distinguishing between points in a quadrant versus on an axis.

Polar Coordinates

Polar coordinates represent a point in the plane using a distance (radius) from a fixed center along with an angle measured from a fixed direction, typically the positive x-axis. This system offers an alternative to rectangular coordinates.

Conversion between Polar and Rectangular Coordinates

To convert from polar to rectangular coordinates, the formulas x = r * cos(theta) and y = r * sin(theta) are used. This process is fundamental to determine the detailed location of a point in the Cartesian plane from its polar description.

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