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 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 376: 31



Work Step by Step

First, we use the product theorem to multiply the absolute values and add the arguments: $(12$ cis $18.5^{\circ})(3$ cis $12.5^{\circ})$ $=12(3)$ cis $(18.5^{\circ}+12.5^{\circ})$ $=36$ cis $(31.0^{\circ})$ Next, we change the expression into its equivalent form: $36$ cis $(31.0^{\circ})$ $=36 (\cos 31^{\circ}+i\sin 31^{\circ})$ Then, we use the calculator to solve the functions of $\cos$ and $\sin$ and simplify the expression: $36 (\cos 31^{\circ}+i\sin 31^{\circ})$ =$36 [0.857167+i(0.515038)]$ =$30.8580+18.5414i$
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