Stitz-Zeager_College_Algebra_e-book

We dene scalar multiplication for vectors in the same

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online