Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set: 80

Answer

$2a+6b+2c$

Work Step by Step

Note that the angles $t+1000\pi$ and $t - 1000\pi$ are both coterminal with the angle $t$ since $1000\pi$is a multiple of $2\pi$. Note further that coterminal angles have the same value for the trigonometric functions. Thus, the given expression is equivalent to $=-\cos{t}+7\cos{t}+\tan{t}+\tan{(t+999\pi)}+\sin{t}+\sin{t}$ Recall that the period of the tangent function is $\pi$. This means that the angles $t$ and $t+999\pi$ have the same value as they are 999 periods apart. Thus, the expression above is equivalent to: $=-\cos{t}+7\cos{t}+\tan{t}+\tan{t}+\sin{t}+\sin{t}$ Use the given to obtain: $=-b+7b+c+c+a+a \\=2a+6b+2c$
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