Stitz-Zeager_College_Algebra_e-book

The intensity of the push or pull is the magnitude of

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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...
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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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