Stitz-Zeager_College_Algebra_e-book

61 the reader may wonder what the rotated form of the

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Unformatted text preview: ich case (r, θ) = (0, θ) is the pole. Since the pole is identified with the origin (0, 0) in rectangular coordinates, the theorem in this case amounts to checking ‘0 = 0.’ The following example puts Theorem 11.7 to good use. • x2 + y 2 = r2 and tan(θ) = Example 11.4.2. Convert each point in rectangular coordinates given below into polar coordinates with r ≥ 0 and 0 ≤ θ < 2π . Use exact values if possible and round any approximate values to two decimal places. Check your answer by converting them back to rectangular coordinates. √ 1. P 2, −2 3 2. Q(−3, −3) 3. R(0, −3) 4. S (−3, 4) Solution. 1. Even though we are not explicitly told to do so, we can avoid many common mistakes by taking √ the time to plot the points before we do any calculations. Plotting P 2, −2 3 shows that 788 Applications of Trigonometry √2 √ it lies in Quadrant IV. With x = 2 and y = −2 3, we get r2 = x2 + y 2 = (2)2 + −2 3 = 4 + 12 = 16 so r = ±4. Since we are asked for r ≥ 0, we choose r = 4. To find θ, we have √ ...
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