9. Polar Equations

Use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (3, 90°)

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 = t − 1

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/4)

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. (3, 4π/3)

In the polar coordinate system, what is the name for a set of coordinates such as the one indicated with $c$ (for example, $(r,\theta )$)?

Plot the point on the polar coordinate system.

$(6,-\(\frac{11\pi}{6}\))$

In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. r = 12 cos θ

In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. (5, 0)

Indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, −135°)

Plot the point $(5,-\(\frac{\pi}{3}\))$, then identify which of the following sets of coordinates is the same point.

In Exercises 81–82, find the rectangular coordinates of each pair of points. Then find the distance, in simplified radical form, between the points. (2, 2π/3) and (4, π/6)

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 = t − 2, y = 2t + 1; −2 ≤ t ≤ 3

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 = 1 + 3 cos t, y = 2 + 3 sin t; 0 ≤ t < 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. (−1, π)

Plot the point on the polar coordinate system.

$(-2,\(\frac{2\pi}{3}\))$