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Stitz-Zeager_College_Algebra_e-book

# In the case of our vector v above any vector which

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Unformatted text preview: hese representations by substituting the values for θ into r = 6 cos(2θ), once again, for illustration purposes. (We feel most students would take this approach.) Again, in the interests of eﬃciency, we could ‘plug’ π π π these values for θ into r = 3 (where there is no θ) and get the list of points: 3, π , 3, 23 , 3, 43 and 3, 53 . 3 While it is not true that 3, π represents the same point as −3, π , we still get the same set of solutions. 3 3 16 A quick sketch of r = 3 sin θ and r = 3 cos θ in the θr-plane will convince you that, viewed as functions of r, 2 2 these are two diﬀerent animals. 15 11.5 Graphs of Polar Equations 813 √ get only one intersection point which can be represented by 3 2 2 , π . We now investigate 2 other representations for the intersection points. Suppose P is an intersection point with θ a representation (r, θ) which satisﬁes r = 3 sin 2 and the same point P has a diﬀerent θ representation (r, θ + 2πk ) for some integer k which satisﬁes r = 3 cos 2 . Substituting θ into the latter, we get r = 3 cos...
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