Answered: Y P (x,y) (E,N) (r,0) be of. X

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Prove That coordinates of P expressed in the E, N coordinate system, which resulted from rotating the X, Y coordinate system by an angle a as shown in the figure, can be expressed as follows.

E = X cos(a) + Y sin(a)

N = Y cos (a) - X sin(a)

Please use the following trigonometric equalities in your proof.

sin(a+/-b) = sin a cos b +/- cos a sin b

cos (a+/-b) = cos a cos b +/- sin a sin b

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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