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: 81

Answer

a. $(0,3)$ b. $3$ c. $-270^{\circ}$

Work Step by Step

a. The terminal side of $90^{\circ}$ in standard position is on the positive $y$ axis. The terminal side is represented by the blue line in the figure. The coordinates of points on the terminal side of $90^{\circ}$ can be given by $(0,a)$, where $a$ is a positive number. Choosing $a=3$ arbitrarily, the point is $(0,3)$. b. To find the distance from the origin to $(0,3)$, we use the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(0-0)^2+(3-0)^2}=\sqrt{9}=3$$ $$\therefore r = 3$$ c. To find an angle that is coterminal with $90^{\circ}$, we traverse a full revolution in the positive or negative direction. Negative coterminal angle = $90^{\circ}-360^{\circ}= -270^{\circ}$
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