Problem 89 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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 1: Drawing the graph

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

Step 2: 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.

Step 3: 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.

Step 4: 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.