In Exercises 13–34, test for symmetry and then graph each polar equation. r = 4 sin 3θ

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − 3 sin θ

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

In Exercises 35–44, test for symmetry and then graph each polar equation. r = cos θ/2

In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ

In Exercises 35–44, test for symmetry and then graph each polar equation. r = 2 + 3 sin 2θ

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 = 3 − 5t, y = 4 + 2t; t = 1

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 = 7 − 4t, y = 5 + 6t; t = 1

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 = t² + 1, y = 5 − t³; t = 2

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 = t² + 3, y = 6 − t³; t = 2

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Line: Passes through (−2,4) and (1,7)

In Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = x² + 4

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Circle: Center: (3,5); Radius: 6

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 = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2

In Exercises 59–62, sketch the plane curve represented by the given parametric equations. Then use interval notation to give each relation's domain and range. x = t² + t + 1, y = 2t

In Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = 4x − 3

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Ellipse: Center: (−2,3); Vertices: 5 units to the left and right of the center; Endpoints of Minor Axis: 2 units above and below the center

In Exercises 41–43, eliminate the parameter. Write the resulting equation in standard form.

A hyperbola: x = h + a sec t, y = k + b tan t

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Hyperbola: Vertices: (4,0) and (−4,0); Foci: (6,0) and (−6,0)

In Exercises 57–58, the parametric equations of four plane curves are given. Graph each plane curve and determine how they differ from each other. x = t and y = t² − 4

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

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 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 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 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 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 = 2 sin t, y = 2 cos t; 0 ≤ t < 2π

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 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 = 2 + 4 cos t, y = −1 + 3 sin t; 0 ≤ t ≤ π

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 = 5 sec t, y = 3 tan t

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 = 2ᵗ, y = 2⁻ᵗ; t ≥ 0