37–52. Curves to parametric equations Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique.
The lower half of the circle centered at (−2, 2) with radius 6, oriented in the counterclockwise direction
73–76. Tangent lines Find an equation of the line tangent to the curve at the point corresponding to the given value of t.
x=t ²−1, y=t ³ +t; t=2
81–88. Arc length Find the arc length of the following curves on the given interval.
x = 2t sin t - t² cos t, y = 2t cos t + t² sin t; 0 ≤ t ≤ π
45–60. Areas of regions Find the area of the following regions.
The region inside the rose r = 4 sin 2θ and inside the circle r = 2
31–36. Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in x and y.
x=tan t, y=sec ² t−1
25–28. Horizontal and vertical tangents Find the points at which the following polar curves have horizontal or vertical tangent lines.
r = 4 cos θ
