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Stitz-Zeager_College_Algebra_e-book

1 is to derive equations for the conic sections using

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Unformatted text preview: e. Example 11.4.1. For each point in polar coordinates given below plot the point and then give two additional expressions for the point, one of which has r > 0 and the other with r < 0. 1. P (2, 240◦ ) π 2. P −4, 76 π 3. P 117, − 52 4. P −3, − π 4 Solution. 1. Whether we move 2 units along the polar axis and then rotate 240◦ or rotate 240◦ then move out 2 units from the pole, we plot P (2, 240◦ ) below. θ = 240◦ Pole Pole P (2, 240◦ ) We now set about ﬁnding alternate descriptions (r, θ) for the point P . Since P is 2 units from the pole, r = ±2. Next, we choose angles θ for each of the r values. The given representation for P is (2, 240◦ ) so the angle θ we choose for the r = 2 case must be coterminal with 240◦ . (Can you see why?) One such angle is θ = −120◦ so one answer for this case is (2, −120◦ ). For the case r = −2, we visualize our rotation starting 2 units to the left of the pole. From this position, we need only to rotate θ = 60◦ to arrive at...
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