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: 32



Work Step by Step

First, we use the product theorem to multiply the absolute values and add the arguments: $(4$ cis $19.25^{\circ})(7$ cis $41.75^{\circ})$ $=4(7)$ cis $(19.25^{\circ}+41.75^{\circ})$ $=28$ cis $(61.0^{\circ})$ Next, we change the expression into its equivalent form: $=28$ cis $(61.0^{\circ})$ $=28 (\cos 61^{\circ}+i\sin 61^{\circ})$ Then, we use the calculator to solve the functions of $\cos$ and $\sin$ and simplify the expression: $28 (\cos 61^{\circ}+i\sin 61^{\circ})$ =$28 [0.484807+i(0.874620)]$ =$13.5747+24.4894i$
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