Calculus- Early Transcendentals, 2021a

404 Polar Coordinates, Parametric Equations
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Figure 11.5: Graph of r = 2sinθ.
Exercises for 11.1
Exercise 11.1.1 Plot these polar coordinate points on one graph: (2,π/3), (−3,π/2), (−2,−π/4),
(1/2,π), (1,4π/3), (0,3π/2).
Exercise 11.1.2 Find an equation in polar coordinates that has the same graph as the given equation in
rectangular coordinates.
(a) y = 3x
(b) y = −4
(c) xy 2 = 1
(d) x 2 + y 2 = 5
(e) y = x 3
(f) y = sinx
(g) y = 5x + 2
(h) x = 2
(i) y = x 2 + 1
Exercise 11.1.3 Sketch the following curves:
(a) r = cosθ
(b) r = 1 + θ 1 /π 2
(c) r = sin(θ + π/4)
(d) r = −secθ
(e) r = θ/2, θ ≥ 0
(f) r = cotθ cscθ
(g) r =
1
sinθ + cosθ
(h) r 2 = −2secθ cscθ
Exercise 11.1.4 Find an equation in rectangular coordinates that has the same graph as the given equation
in polar coordinates.
(a) r = sin(3θ)
(b) r = sin 2 θ
(c) r = secθ cscθ
(d) r = tanθ