Stitz-Zeager_College_Algebra_e-book

B prove that z z z zz zz c show that rez and

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ircle, centered at the origin, with a radius of 2. The graph of r = 3 cos(θ) is also a circle - but this one is centered at the point 3 with rectangular coordinates 3 , 0 and has a radius of 2 . 2 y 2 −2 2 3 x −2 r = 2 and r = 3 cos(θ ) We have two intersection points to ﬁnd, one in Quadrant I and one in Quadrant IV. Proceeding as above, we ﬁrst determine if any of the intersection points P have a representation (r, θ) which satisﬁes both r = 2 and r = 3 cos(θ). Equating these two expressions for r, we get cos(θ) = 2 . To solve this equation, we need the arccosine function. We get 3 11 We are really using the technique of substitution to solve the system of equations r r = = 2 sin(θ) 2 − 2 sin(θ) 11.5 Graphs of Polar Equations 811 2 θ = arccos 2 + 2πk or θ = 2π − arccos 3 + 2πk for integers k . From these solutions, we get 3 2 2, arccos 3 as one representation for our answer in Quadrant I, and 2, 2π − arccos 2 3 as one representation for our answer in Quadrant IV. The reader is enc...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online