Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - Test - Page 651: 20

Answer

(a) $cos(\frac{x}{2})+1$ (b) $-\frac{1}{2}cot(x)$

Work Step by Step

Compare with the standard graphs of the six basic circular functions and examine the amplitude, period, vertical shift and reflection around the axes of each graph, we have: (a) Amplitude $1$, period $4\pi$, vertical shift $1$, thus $y=cos(\frac{x}{2})+1$ (b) Period $\pi$, $f(\frac{\pi}{4})=-\frac{1}{2}$, thus $y=-\frac{1}{2}cot(x)$
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