Trigonometry (11th Edition) Clone

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

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.6 Parametric Equations, Graphs, and Applications - 8.6 Exercises - Page 404: 26

Answer

(a) $x = t-3$ $y = \frac{2}{t-3}$ (Note that $t \neq 3$) We can see the graph below. (b) $y = \frac{2}{x}$ $x\neq 0$
1531208404

Work Step by Step

(a) $x = t-3$ $y = \frac{2}{t-3}$ $t \neq 3$ t = -1: $x = (-1)-3 = -4$ $y = \frac{2}{(-1)-3} = -\frac{1}{2}$ t = 0: $x = (0)-3 = -3$ $y = \frac{2}{(0)-3} = -\frac{2}{3}$ t = 1: $x = (1)-3 = -2$ $y = \frac{2}{(1)-3} = -1$ t = 2: $x = (2)-3 = -1$ $y = \frac{2}{(2)-3} = -2$ $t = \frac{5}{2}$: $x = (\frac{5}{2})-3 = -\frac{1}{2}$ $y = \frac{2}{(\frac{5}{2})-3} = -4$ $t = \frac{7}{2}$: $x = (\frac{7}{2})-3 = \frac{1}{2}$ $y = \frac{2}{(\frac{7}{2})-3} = 4$ t = 4: $x = (4)-3 = 1$ $y = \frac{2}{(4)-3} = 2$ t = 5: $x = (5)-3 = 2$ $y = \frac{2}{(5)-3} = 1$ t = 6: $x = (6)-3 = 3$ $y = \frac{2}{(6)-3} = \frac{2}{3}$ t = 7: $x = (7)-3 = 4$ $y = \frac{2}{(7)-3} = \frac{1}{2}$ We can see the graph below. (b) $x = t-3$ $y = \frac{2}{t-3}$ Therefore: $~~y = \frac{2}{x}$ Since $t \neq 3$, then $x\neq 0$
Small 1531208404
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