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: 78

Answer

$-a +b + c$

Work Step by Step

Note that the angles $-t-2\pi$ and $-t - 4\pi$ are both coterminal with the angle $-t$ since $2\pi$ and $4\pi$ are multiples of $2\pi$. Note further that coterminal angles have the same value for the trigonometric functions. Thus, the given expression is equivalent to $=\sin{(-t)} + \cos{(-t)} - \tan{(-t-\pi)}$ Recall that the period of the tangent function is $\pi$. This means that the angles $-t$ and $-t-\pi$ have the same value as they are one period apart. Thus, the expression above is equivalent to: $=\sin{(-t)} + \cos{(-t)} - \tan{(-t)}$ RECALL: (1) $\sin{(-t)} = -\sin{t}$ (2) $\cos{(-t)} = \cos{t}$ (3) $\tan{(-t)} = -\tan{t}$ Use the given and rules above to obtain: $=-\sin{t} + \cos{t} -(-\tan{t}) \\=-\sin{t} + \cos{t} + \tan{t} \\=-a +b + c$
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