SECTION 9.2 Polar Equations and Graphs 613 The smaller step θ is the more points the graphing utility plots. Experiment with different values for min, θ max, θ and step θ to see how the graph is affected. Step 3 Enter the expression 2 sinθ after the prompt = r . Step 4 Graph. Figure 26(a) shows the graph using a TI-84 Plus CE. Figure 26(b) shows the graph using Desmos. Desmos does not require that we solve for r, but does require a range for the values of .θ The wrench icon in Desmos provides the ability to change the type of grid from rectangular to polar. Examples 3, 4, and 5 lead to the following results. (The proofs are left as exercises. See Problems 83 and 84.) (b) Figure 26 θ = rsin 2 5 25 28 8 r1 5 2 sin u (a) Identifying and Graphing a Polar Equation (Vertical Line) Identify and graph the equation: rcos 3 θ = − Solution EXAMPLE 5 Since x rcos ,θ = we can write the equation as x 3 = − Therefore, the graph of rcos 3 θ = − is a vertical line 3 units to the left of the pole. Figure 27(a) shows the graph drawn by hand. Figure 27(b) shows the graph using Desmos. Figure 27 θ = − = − r x cos 3, or 3 (a) (b) x O y 2 4 5 u 5 0 u 5 p u 5 1 3 1 2 3 4 5 p– 2 u 5 3p –– 2 u 5 7p –– 4 u 5 p– 4 u 5 3p –– 4 u 5 5p –– 4
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