Answered: Graph one complete cycle for each of…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Graph one complete cycle for each of the following. In each case, label the axes accurately
and state the period for each graph.

y = 1/2 sec 3 x

Expert Solution

Step 1

Consider the given function

$y = \frac{1}{2} s e c 3 x$

Since the period of $s e c x$ is $2 π$

Therefor, the period of the given function $y = \frac{1}{2} s e c 3 x$ is $\frac{2 π}{3}$ .

And the one complete cycle of the function starts from $x = 0 and ends to x = \frac{2 π}{3}$

Now divide the period by 4, then the input becomes $\frac{π}{6}$

Then, arrange the set of inputs starting from $x = 0 and then x = 1 \times \frac{π}{6}, x = 2 \times \frac{π}{6}, x = 3 \times \frac{π}{6}, x = 4 \times \frac{π}{6}$

$x = 0, \frac{π}{6}, \frac{π}{3}, \frac{π}{2}, \frac{2 π}{3}$

So, the set of inputs for one complete cycle is,

$x = 0, \frac{π}{6}, \frac{π}{3}, \frac{π}{2}, \frac{2 π}{3}$

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