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Stitz-Zeager_College_Algebra_e-book

# We have our new denition below definition 111 given a

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Unformatted text preview: the angle ﬁrst, we rotate π radians, then move back through the pole 3.5 units. 4 π Here we are locating a point 3.5 units away from the pole on the terminal side of 54 , not π . 4 θ= π 4 Pole θ= π 4 Pole Pole Q −3.5, π 4 As you may have guessed, θ < 0 means the rotation away from the polar axis is clockwise instead π of counter-clockwise. Hence, to plot R 3.5, − 34 r = 3.5 Pole Pole Pole π θ = − 34 π R 3.5, − 34 π From an ‘angles ﬁrst’ approach, we rotate − 34 then move out 3.5 units from the pole. We see R is 3π the point on the terminal side of θ = − 4 which is 3.5 units from the pole. Pole π θ = − 34 Pole Pole π θ = − 34 π R 3.5, − 34 784 Applications of Trigonometry The points Q and R above are, in fact, the same point despite the fact their polar coordinate representations are diﬀerent. Unlike Cartesian coordinates where (a, b) and (c, d) represent the same point if and only if a = c and b = d, a point can be represented by inﬁnitely many polar coordinate pairs. We explore this notion more in the following exampl...
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