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Stitz-Zeager_College_Algebra_e-book

# The quadratic factor gives two more cube roots w 1 i 3

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Unformatted text preview: egion between the line θ = 3 and the x-axis in Quadrant IV. 804 Applications of Trigonometry r y 6 θ= 4 4π 3 2 x 2π 3 4π 3 π π 2 3π 2 2π θ −2 ππ On the interval 43 , 32 , r returns to positive values and increases from 0 to 2. We hug the 4π line θ = 3 as we move through the origin and head towards negative y -axis. r y 6 θ= 4 2 4π 3 x 4π 3 2π 3 π π 2 3π 2 2π θ −2 π As we round out the interval, we ﬁnd that as θ runs through 32 to 2π , r increases from 2 out to 6, and we end up back where we started, 6 units from the origin on the positive x-axis. r y 6 4 2 x 2π 3 π 2 4π 3 π 3π 2 2π θ θ runs from −2 3π 2 to 2π 11.5 Graphs of Polar Equations 805 Again, we invite the reader to show that plotting the curve for values of θ outside [0, 2π ] results in retracing a portion of the curve already traced. Our ﬁnal graph is below. r y 6 4 θ= 2π 3 2 2 2π 3 2 4π 3 π π 2 2π 3π 2 θ θ= 6 x 4π 3 −2 −2 r = 2 + 4 cos(θ) in the θr-plane r = 2 + 4 cos(θ) in the xy -plane 3. As usual, we start by graphing a fundamental cycle...
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