Also, when = 0, 1 + 3sin(θ) = 0, so: r sin(θ) = - 0.34 + 2kπ θ ≈ (- 0.34) + 2kπ = + 0.34 + 2kπ , is an integer. θ ≈ π – π k So a graph of the equation is a limaçon symmetric about the y- axis. 61. We’ll start with a table of values. - 0 θ π π - 2π - 0 2π r π π Observe that as increases its absolute so does Therefore a graph of the equation should r. θ contain two spiral curves that are symmetric about the y- axis. 63. We’ll start with a table of values. 0 2π θ π 4 3 + 5 1 3 - 2 3 - 1 undef. 5 3 + 4 r Also, when = 0, 3 + sec(θ) = 0, so: r sec(θ) = - 3 1.9106 + 2kπ θ ≈ 2π - 1.9106 + 2kπ 4.3726 + 2kπ, where is an integer. k θ ≈ ≈ So a of the equation is a conchoid symmetric about the x-axis.
Also, when r = 0, 1 + 3sin(θ) = 0, so: sin(θ) = θ ≈ - 0.34 + 2kπ θ ≈ π – (- 0.34) + 2kπ = π + 0.34 + 2kπ , k is an integer. So a graph of the equation is a limaçon symmetric about the y- axis. 61. We’ll start with a table of values. θ - π 0 π r - 2π - π 0 π 2π Observe that as θ increases its absolute so does r. Therefore a graph of the equation should contain two spiral curves that are symmetric about the y- axis. θ 0 π 2π r 4 3 + 5 1 3 - 2 3 - 1 undef. 5 3 + 4 63. We’ll start with a table of values. Also, when r = 0, 3 + sec(θ) = 0, so: sec(θ) = - 3 θ ≈ 1.9106 + 2kπ θ ≈ 2π - 1.9106 + 2kπ ≈ 4.3726 + 2kπ, where k is an integer. So a of the equation is a conchoid symmetric about the x-axis.
Chapter%208%20Solutions.docx