Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Review Exercises - Page 411: 71

Answer

$x = t+cos~t$ $y = sin~t$ $t$ in $[0,2\pi]$ We can see the graph below:
1530865879

Work Step by Step

$x = t+cos~t$ $y = sin~t$ $t$ in $[0,2\pi]$ When $t = 0$: $x = 0 + cos~0 = 1$ $y = sin~0 = 0$ When $t = \frac{\pi}{4}$: $x = \frac{\pi}{4} + cos~\frac{\pi}{4} = \frac{\pi}{4} + \frac{\sqrt{2}}{2} = 1.49$ $y = sin~\frac{\pi}{4} = \frac{\sqrt{2}}{2} = 0.707$ When $t = \frac{\pi}{2}$: $x = \frac{\pi}{2} + cos~\frac{\pi}{2} = \frac{\pi}{2}+0 = 1.57$ $y = sin~\frac{\pi}{2} = 1$ When $t = \frac{3\pi}{4}$: $x = \frac{3\pi}{4} + cos~\frac{3\pi}{4} = \frac{3\pi}{4} -\frac{\sqrt{2}}{2} = 1.65$ $y = sin~\frac{3\pi}{4} = \frac{\sqrt{2}}{2} = 0.707$ When $t = \pi$: $x = \pi + cos~\pi = \pi-1 = 2.14$ $y = sin~\pi = 0$ When $t = \frac{5\pi}{4}$: $x = \frac{5\pi}{4} + cos~\frac{5\pi}{4} = \frac{5\pi}{4} -\frac{\sqrt{2}}{2} = 3.22$ $y = sin~\frac{5\pi}{4} = -\frac{\sqrt{2}}{2} = -0.707$ When $t = \frac{3\pi}{2}$: $x = \frac{3\pi}{2} + cos~\frac{3\pi}{2} = \frac{3\pi}{2}+0 = 4.71$ $y = sin~\frac{3\pi}{2} = -1$ When $t = \frac{7\pi}{4}$: $x = \frac{7\pi}{4} + cos~\frac{7\pi}{4} = \frac{7\pi}{4} +\frac{\sqrt{2}}{2} = 6.20$ $y = sin~\frac{7\pi}{4} = -\frac{\sqrt{2}}{2} = -0.707$ When $t = 2\pi$: $x = 2\pi + cos~2\pi = 2\pi+1 = 7.28$ $y = sin~0 = 0$ We can see the graph below:
Small 1530865879
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