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Problem 8.27
For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. See Examples 1 and 2.
x = t + 2 , y = t ―4 , for t in (― ∞ , ∞)
Problem 8.30
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.
x = 2 cos t , y = 2 sin t
Problem 8.32
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.
x = 4 sin t , y = 3 cos t
Problem 8.33
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.
x = 2 + sin t , y = 1 + cos t
Problem 8.34
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.
x = 1 + cos t , y = sin t ― 1
Problem 13c
For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).
(1 , 45°)
Problem 14c
For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).
(3 , 120°)
Problem 17c
For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).
(5 , ―60°)
Problem 19c
For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).
(―3 , ―210°)
Problem 22c
For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).
(4 , 3π/2)
Problem 44
Match each equation with its polar graph from choices A–D.
r = cos 3θ
Problem 45
Match each equation with its polar graph from choices A–D.
r = cos 2θ
Problem 46
Match each equation with its polar graph from choices A–D.
r = 2/(cosθ + sinθ)
Problem 47
Graph each polar equation. Also, identify the type of polar graph.
r = 2 + 2 cos θ
Problem 59
Graph each polar equation. Also, identify the type of polar graph.
r² = 4 cos 2θ