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**Unformatted text preview: **g the polar axis 117 units from the pole and rotate
π
clockwise 52 radians as illustrated below. Pole Pole
π
θ = − 52 π
P 117, − 52 Since P is 117 units from the pole, any representation (r, θ) for P satisﬁes r = ±117. For the
π
r = 117 case, we can take θ to be any angle coterminal with − 52 . In this case, we choose
π
π
θ = 32 , and get 117, 32 as one answer. For the r = −117 case, we visualize moving left 117
units from the pole and then rotating through an angle θ to reach P . We ﬁnd θ = π satisﬁes
2
this requirement, so our second answer is −117, π .
2 Pole
θ= Pole 3π
2 θ= P 117, 3π
2 π
2 P −117, π
2 786 Applications of Trigonometry 4. We move three units to the left of the pole and follow up with a clockwise rotation of
π
radians to plot P −3, − π . We see that P lies on the terminal side of 34 .
4 π
4 P −3, − π
4 θ = −π
4
Pole Pole π
π
Since P lies on the terminal side of 34 , one alternative representation for P is 3, 34 . To
ﬁnd a diﬀerent represe...

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