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: 78

Answer

a. $(3,3)$ b. $3\sqrt{2}$ c. $405^{\circ}$

Work Step by Step

a. The terminal side of $45^{\circ}$ in standard position is in the 1st quadrant. It lies along the line $y=x$. The terminal side is represented by the blue line in the figure. The coordinates of points on the terminal side of $45^{\circ}$ 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 $45^{\circ}$, we traverse a full revolution in the positive or negative direction. Positive coterminal angle = $45^{\circ}+360^{\circ}= 405^{\circ}$
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