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: 79

Answer

$3a+2b-2c$

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 $=\cos{t}+\cos{t}-\tan{t}-\tan{(t+999\pi)}-\sin{t}+4\sin{t}$ 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: $=\cos{t}+\cos{t}-\tan{t}-\tan{t}-\sin{t}+4\sin{t}$ Use the given to obtain: $=b+b-c-c-a+4a \\=3a+2b-2c$
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