The intensity of the push or pull is the magnitude of

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: More specifically, it is the hyperbola obtained by rotating the graph of x2 − y 2 = 4 counter-clockwise through a 45◦ angle. Armed with polar coordinates, we can generalize the process of rotating axes as shown below. 11.6.1 Rotation of Axes Consider the x- and y -axes below along with the dashed x - and y -axes obtained by rotating the xand y -axes counter-clockwise through an angle θ and consider the point P (x, y ). The coordinates (x, y ) are rectangular coordinates and are based on the x- and y -axes. Suppose we wished to find rectangular coordinates based on the x - and y -axes. That is, we wish to determine P (x , y ). While this seems like a formidable challenge, it is nearly trivial if we use polar coordinates. Consider the angle φ whose initial side is the positive x -axis and whose terminal side contains the point P . y y P (x, y ) = P (x , y ) x θ φ θ x We relate P (x, y ) and P (x , y ) by converting them to polar coordinates. Converting P (x, y ) to polar coordinates with r > 0 yields x = r cos(θ + φ) and...
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