B for z 2 4i z 2 5 and arctan2 hence

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Unformatted text preview: n r = 4, θ is free. The graph of this equation is, therefore, all points which have a polar coordinate representation (4, θ), for any choice of θ. Graphically this translates into tracing out all of the points 4 units away from the origin. This is exactly the definition of circle, centered at the origin, with a radius of 4. y y 4 θ>0 x θ<0 −4 4 x −4 In r = 4, θ is free The graph of r = 4 √ 2. Once again we have θ being free in the equation r = −3 2. Plotting all of the points of the √ √ form (−3 2, θ) gives us a circle of radius 3 2 centered at the origin. 1 See the discussion in Example 11.4.3 number 2a. 11.5 Graphs of Polar Equations 797 y y 4 θ<0 x θ>0 −4 4 x −4 √ In r = −3 2, θ is free √ The graph of r = −3 2 π π 3. In the equation θ = 54 , r is free, so we plot all of the points with polar representation r, 54 . π What we find is that we are tracing out the line which contains the terminal side of θ = 54 when plotted in standard position. y y 4 r<0 θ= 5π 4 r=0 x −4 4 x r>0 −4 In θ = 5π 4, r is free Th...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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