Question 6.3.1: Plotting Points in a Polar Coordinate System Plot the points...
Plotting Points in a Polar Coordinate System
Plot the points with the following polar coordinates:
a. (2, 135°) b. (-3, \frac{3 \pi}{2}) c. (-1, -\frac{\pi}{4}).
a. To plot the point (r, θ) = (2, 135°), begin with the 135° angle. Because 135° is a positive angle, draw θ = 135° counterclockwise from the polar axis. Now consider r = 2. Because r > 0, plot the point by going out two units on the terminal side of θ. Figure 6.22(a) shows the point. The concentric circles in the figure are drawn to help plot the point at the appropriate distance from the pole.
b. To plot the point (r, θ) = (-3, \frac{3 \pi}{2}), begin with the \frac{3 \pi}{2} angle. Because \frac{3 \pi}{2} is a positive angle, we draw \theta=\frac{3 \pi}{2} counterclockwise from the polar axis. Now consider r = -3. Because r < 0, plot the point by going out three units along the ray opposite the terminal side of θ. Figure 6.22(b) shows the point.
c. To plot the point (r, θ) = (-1, -\frac{\pi}{4}), begin with the -\frac{\pi}{4} angle. Because -\frac{\pi}{4} is a negative angle, draw \theta=-\frac{\pi}{4} clockwise from the polar axis. Now consider r = -1. Because r < 0, plot the point by going out one unit along the ray opposite the terminal side of θ. Figure 6.22(c) shows the point.
