Stitz-Zeager_College_Algebra_e-book

Viewing the common initial point of these vectors as

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: y = r sin(θ + φ). To convert the point P (x , y ) into polar coordinates, we first match the polar axis with the positive x -axis, choose the same r > 0 (since the origin is the same in both systems) and get x = r cos(φ) and y = r sin(φ). Using the sum formulas for sine and cosine, we have x = r cos(θ + φ) = r cos(θ) cos(φ) − r sin(θ) sin(φ) Sum formula for cosine = (r cos(φ)) cos(θ) − (r sin(φ)) sin(θ) = x cos(θ) − y sin(θ) Since x = r cos(φ) and y = r sin(φ) 11.6 Hooked on Conics Again 827 Similarly, using the sum formula for sine we get y = x sin(θ) + y cos(θ). These equations enable us to easily convert points with x y -coordinates back into xy -coordinates. They also enable us to easily convert equations in the variables x and y into equations in the variables in terms of x and y .1 If we want equations which enable us to convert points with xy -coordinates into x y -coordinates, we need to solve the system x cos(θ) − y sin(θ) = x x sin(θ) + y cos(θ) = y for x and y . Perhaps the cle...
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