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Chapter 8: Problem 5

Graph the point on a polar grid. $$\left(1, \frac{\pi}{6}\right)$$

Short Answer

Expert verified
Plot the point 1 unit from the origin at a 30掳 angle.

Step by step solution

01

- Understand the Polar Coordinates

Polar coordinates are represented as \(r, \theta\), where \(r\) is the radial distance from the origin (center of the polar grid), and \(\theta\) is the angle measured counterclockwise from the positive x-axis.
02

- Identify the Radial Distance

In the given point \(1, \frac{\pi}{6}\), identify \(r\) as the radial distance. Here, \(r = 1\). This means the point is 1 unit away from the origin.
03

- Identify the Angle

Identify \(\theta\) as the angle. In the given point \(1, \frac{\pi}{6}\), \(\theta = \frac{\pi}{6}\) radians. This angle needs to be converted to degrees if needed. \(\frac{\pi}{6} = 30^\text{o}\).
04

- Locate the Angle on the Polar Grid

On the polar grid, locate the angle \(\theta = \frac{\pi}{6}\) or 30 degrees. This is the line that makes a 30-degree angle with the positive x-axis.
05

- Measure the Radial Distance

From the angle line located in step 4, measure a distance of 1 unit away from the origin along this line.
06

- Plot the Point

Mark the point where you measured the radial distance from the origin. This is the point \(1, \frac{\pi}{6}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radial Distance
To understand polar coordinates better, let's dive into one of the core concepts: radial distance. Radial distance, represented by the variable \(r\), refers to how far a point is from the origin (or center) of the polar grid. In the Cartesian coordinate system (the traditional x-y plane), distance is typically discussed horizontally and vertically. However, in the polar coordinate system, it's all about this radial distance from the center.

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