9. Polar Equations

In Exercises 27–32, select the representations that do not change the location of the given point. (−6, 3π) (6, −π)

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − sin θ

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

x³ − (1 + i√3) = 0

In calculus, it can be shown that e^(iθ) = cos θ + i sin θ. In Exercises 87–90, use this result to plot each complex number. -e^-πi

In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ < t < ∞

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 = 2 + 3 cos t, y = 4 + 2 sin t; t = π

In Exercises 27–32, select the representations that do not change the location of the given point. (2, − 3π/4) (2, − 7π/4)

In Exercises 79–80, convert each polar equation to a rectangular equation. Then determine the graph's slope and y-intercept.

r sin (θ − π/4) = 2

Graph each polar equation. r = 1 + sin θ

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

x⁴ + 16i = 0

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 + 2 cos θ

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

In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which

a. r>0, 2π < θ < 4π.

b. r<0, 0. < θ < 2π.

c. r>0, −2π. < θ < 0.

(5, π/6)

Plot the point $(-3,-\(\frac{\pi}{6}\))$, then identify which of the following sets of coordinates is the same point.