Stitz-Zeager_College_Algebra_e-book

# We dene scalar multiplication for vectors in the same

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Unformatted text preview: os(θ) (c) Rose: r = 2 sin(2θ) (l) Cardioid: r = 1 − sin(θ) (d) Rose: r = 4 cos(2θ) (m) Lima¸on: r = 1 − 2 cos(θ) c (e) Rose: r = 5 sin(3θ) (f) Rose: r = cos(5θ) (n) Lima¸on: r = 1 − 2 sin(θ) c √ (o) Lima¸on: r = 2 3 + 4 cos(θ) c (g) Rose: r = sin(4θ) (p) Lima¸on: r = 2 + 7 sin(θ) c (h) Rose: r = 3 cos(4θ) (q) Lemniscate: r2 = sin(2θ) (i) Cardioid: r = 3 − 3 cos(θ) (r) Lemniscate: r2 = 4 cos(2θ) 2. Find the exact polar coordinates of the points of intersection of the following pairs of polar equations. Remember to check for intersection at the pole. (a) r = 2 sin(2θ) and r = 1 (d) r = 1 − 2 cos(θ) and r = 1 (b) r = 3 cos(θ) and r = 1 + cos(θ) (e) r = 3 cos(θ) and r = sin(θ) (c) r = 1 + sin(θ) and r = 1 − cos(θ) (f) r2 = 2 sin(2θ) and r = 1 3. Sketch the region in the xy -plane described by the following sets. (a) (r, θ) : 1 + cos(θ) ≤ r ≤ 3 cos(θ), − π ≤ θ ≤ 3 (b) (r, θ) : 1 ≤ r ≤ 2 sin(2θ), 13π 12 ≤θ≤ π 3 17π 12 4. Use set-builder notation to describe the following polar regions. (a) The left half of the circle r = 6 sin(θ) (b) The top half of the cardioid r = 3 − 3 cos(θ) (c) The inside of the petal of the rose r = 3 cos(4θ...
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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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