Unformatted text preview: egion between the line θ = 3 and the xaxis 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 xaxis.
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 θrplane r = 2 + 4 cos(θ) in the xy plane 3. As usual, we start by graphing a fundamental cycle...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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