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: 75

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: $=\sin{t} - \cos{t} + \tan{t}$ Use the given to obtain: $=a - b + c$
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