Problem 77E

Equations of lines Use the result of Exercise 76 to describe and graph the following lines.

r cos (θ − π/3) = 3

Exercise 76

Lines in polar coordinates

a. Show that an equation of the line y = mx + b in polar coordinate is .

Use the figure to find an alternate polar equation of a line, . Note that Q(r0, θ0) is a fixed point on the line such that OQ is perpendicular to the line and r0 ≥ 0; P(r, θ) is an arbitrary point on the line.

Solution 77E

Step 1:

We have to show that r cos (θ − π/3) = 3 by using the following result

Lines in polar coordinates

a. Show that an equation of the line y = mx + b in polar coordinate is .

Use the figure to find an alternate polar equation of a line, . Note that Q(r0, θ0) is a fixed point on the line such that OQ is perpendicular to the line and r0 ≥ 0; P(r, θ) is an arbitrary point on the line.