9. Polar Equations

In Exercises 61–63, test for symmetry with respect to

a. the polar axis.

b. the line θ = π/2.

c. the pole.

r = 5 + 3 cos θ

In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangular form. x⁶ − 1 = 0

Plot the point $(3,\(\frac{\pi}{2}\))$ & find another set of coordinates, $(r,θ)$, for this point, where:

(A) $r≥0,2π≤θ≤4π$,

(B) $r≥0,-2π≤θ≤0$,

(C) $r≤0,0≤θ≤2π$.

In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−2, − π/2)

In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = t, y = 2t

In Exercises 27–32, select the representations that do not change the location of the given point. (−2, 7π/6) (−2, −5π/6)

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 − 3 sin θ

Given the polar equation $r=7\cos \left(\theta \right)$, which of the following is the corresponding Cartesian equation?

Given the point with polar coordinates $(3,\frac{\pi }{4})$, which of the following polar coordinate pairs labels the same point?

Which of the following is a polar equation for the curve represented by the Cartesian equation $x^2+y^2=3$?

Test for symmetry and then graph each polar equation. r = 2 cos θ

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = (60 cos 30°)t, y = 5 + (60 sin 30°)t − 16t²; t = 2

Given the point with polar coordinates $(3,\frac{\pi }{4})$, which of the following polar coordinate pairs labels the same point?

In Exercises 13–34, test for symmetry and then graph each polar equation. r cos θ = −3

Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of θ.