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Chapter 7: Problem 89

Explain how to plot \((r, \theta)\) if \(r>0\) and \(\theta>0\)

Short Answer

Expert verified
Start by drawing a Cartesian plane. Plot a point \(r\) units from the origin along the x-axis. Use this point to draw a circle of radius \(r\). Measure an angle \(\theta\) in counterclockwise direction from the x-axis and draw a line across the circle from the origin at this angle to find the location point \((r, \theta)\)

Step by step solution

01

Drawing the graph

Start by drawing a standard Cartesian plane with both x and y axes. Mark the origin point (0, 0).
02

Plotting the radius

Next, from the origin plot a distance equal to \(r\) units along the positive x-axis. Remember, \(r\) is a positive value and represents the distance of the point from the origin.
03

Drawing the angle

Draw a line from the origin to the plotted point which forms a straight line along the x-axis. The angle \(\theta\) will be calculated counter-clockwise from this line. Measure an angle of \(\theta\) radians (or degrees) in counter-clockwise direction.
04

Finding the point

From the point on the x-axis, draw a line at an angle of \(\theta\) above the x-axis. The point where this line crosses the circle with radius \(r\), is the location of the point \((r, \theta)\) in polar coordinates.

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