Stitz-Zeager_College_Algebra_e-book

Moving one to the right and two down we nd the

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Unformatted text preview: he origin (pole). • Solve for pairs (r, θ) which satisfy both E1 and E2 . • Substitute (θ + 2πk ) for θ in either one of E1 or E2 (but not both) and solve for pairs (r, θ) which satisfy both equations. Keep in mind that k is an integer. • Substitute (−r) for r and (θ + (2k + 1)π ) for θ in either one of E1 or E2 (but not both) and solve for pairs (r, θ) which satisfy both equations. Keep in mind that k is an integer. 814 Applications of Trigonometry Our last example ties together graphing and points of intersection to describe regions in the plane. Example 11.5.4. Sketch the region in the xy -plane described by the following sets. 1. (r, θ) : 0 ≤ r ≤ 5 sin(2θ), 0 ≤ θ ≤ π 2 2. (r, θ) : 3 ≤ r ≤ 6 cos(2θ), 0 ≤ θ ≤ π 6 3. (r, θ) : 2 + 4 cos(θ) ≤ r ≤ 0, 4. (r, θ) : 0 ≤ r ≤ 2 sin(θ), 0 ≤ θ ≤ 2π 3 ≤θ≤ π 6 4π 3 ∪ (r, θ) : 0 ≤ r ≤ 2 − 2 sin(θ), π 6 ≤θ≤ π 2 Solution. Our first step in these problems is to sketch t...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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