612 CHAPTER 9 Polar Coordinates; Vectors Identifying and Graphing a Polar Equation (Horizontal Line) Identify and graph the equation: rsin 2 θ = EXAMPLE 3 Solution Because y rsin ,θ = we can write the equation as y 2 = Therefore, the graph of rsin 2 θ = is a horizontal line 2 units above the pole. See Figure 25. Figure 25 θ = r sin 2 or = y 2 x 2 3 4 5 O y 1 u 5 0 u 5 p u 5 p– 2 u 5 3p –– 2 u 5 7p –– 4 u 5 p– 4 u 5 3p –– 4 u 5 5p –– 4 2 Graph Polar Equations Using a Graphing Utility The following steps are used to graph polar equations on many graphing utilities. Consult your user’s manual for your graphing utility. Graphing a Polar Equation Using a Graphing Utility Step 1 Solve the equation for r in terms of .θ Step 2 Select the viewing window in POLar mode. In addition to setting Xmin, Xmax, Xscl, and so forth, the viewing window in polar mode requires setting minimum and maximum values for θ and an increment setting for step . θ θ( ) Finally, a square screen and radian measure should be used. Step 3 Enter the expression involving θ that you found in Step 1. (Consult your manual for the correct way to enter the expression.) Step 4 Press graph. Graphing a Polar Equation Using a Graphing Utility Use a graphing utility to graph the polar equation rsin 2. θ = Solution EXAMPLE 4 Step 1 Solve the equation for r in terms of .θ r r sin 2 2 sin θ θ = = Step 2 From the polar mode, select a square viewing window. We use the one given next. θ θ π θ π = =− =− = = = = = = X Y X Y X Y min 0 min 8 min 5 max 2 max 8 max 5 step 24 scl 1 scl 1 step θ determines the number of points the graphing utility plots. For example, if step θ is 24 , π then the graphing utility evaluates r at 0 min, 24 , 2 24 , 3 24 , θ θ π π π ( ) = and so forth, up to 2 max . π θ( )
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