Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.2 - The Rectangular Coordinate System - 1.2 Problem Set - Page 26: 77


a. $(-3,3)$ b. $3\sqrt{2}$ c. $-225^{\circ}$

Work Step by Step

a. The terminal side of $135^{\circ}$ in standard position is in the 2nd. It lies along the line $y=-x$ where the $x$ coordinate is negative and the $y$ coordinate is positive. The terminal side is represented by the blue line in the figure. The coordinates of points on the terminal side of $135^{\circ}$ can be given by $(-a,a)$, where $a$ is a positive number. Choosing $a=3$ arbitrarily, the point is $(-3,3)$. b. To find the distance from the origin to $(-3,3)$, we use the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(-3-0)^2+(3-0)^2}=\sqrt{18}=\sqrt{9\times2}$$ $$\therefore r = 3\sqrt{2}$$ c. To find an angle that is coterminal with $135^{\circ}$, we traverse a full revolution in the positive or negative direction. Negative coterminal angle = $135^{\circ}-360^{\circ}= -225^{\circ}$
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