Stitz-Zeager_College_Algebra_e-book

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online