Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problem $85 a n d 86$ graph each of the function
$g (x) = \{\begin{cases} 2 \sin x i f 0 \leq x \leq π \\ \cos x + 1 i f π < x \leq 2 π \end{cases}$

Graph of the given function

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1.Given information

The given function $g (x) = \{\begin{cases} 2 \sin x i f 0 \leq x \leq π \\ \cos x + 1 i f π < x \leq 2 π \end{cases}$

Now graph each function as follows.
The given function is a composite function of function $y = 2 \sin x$ for the interval $0 \leq x \leq π$

and function $y = \cos x + 1$ for the interval $π < x \leq 2 π$ .

Here domain of the function $g (x)$ is $[0, 2 π]$ and its range is 1 to - 1.

Step 2.Calculate some points for sinx in their given domain

Choose different x-values and calculate the corresponding $y = \sin x$ values.

x	y=2sinx	(x,y)
0	$2 \sin 0 = 0$	$(0, 0)$
$\frac{π}{4}$	$2 \sin (\frac{π}{4}) = 2 \frac{\sqrt{2}}{2} = \sqrt{2}$	$(\frac{π}{4}, \sqrt{2})$
$\frac{π}{2}$	$2 \sin (\frac{π}{2}) = 2 (1) = 2$	$(\frac{π}{2}, 2)$
$\frac{3 π}{4}$	$2 \sin (\frac{3 π}{4}) = 2 \frac{\sqrt{2}}{2} = \sqrt{2}$	$(\frac{3 π}{4}, \sqrt{2})$
$π$	$2 \sin (π) = 0$	$(π, 0)$

Step 3.Calculate some points for cosx in their given domain

Choose different -xvalues and calculate the

y = \cos x + 1

corresponding values.

$x$	$y = \cos x + 1$	$(x, y)$
$\frac{5 π}{4}$	$\cos (\frac{5 π}{4}) + 1 = - \frac{\sqrt{2}}{2} + 1 = 0.293$	$(\frac{5 π}{4}, 0.293)$
role="math" localid="1646328747587" $\frac{3 π}{2}$	$\cos (\frac{3 π}{2}) + 1 = 0 + 1 = 1$	$(\frac{3 π}{2}, 1)$
$\frac{7 π}{4}$	$\cos (\frac{7 π}{4}) = \frac{\sqrt{2}}{2} + 1 = 1.7071$	$(\frac{7 π}{4}, 1.7071)$
$2 π$	$\cos (2 π) + 1 = 1 + 1 = 2$	$(2 π, 2)$

Step 4.Plot the above ordered pairs on the graph and connect them with a smooth curve.

Thus function $g (x)$ is graphed as a composite function of $y = 2 \sin x$ in blue and $y = \cos x + 1$ in pink shown below:

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problem $85 a n d 86$ graph each of the function
$g (x) = \{\begin{cases} 2 \sin x i f 0 \leq x \leq π \\ \cos x + 1 i f π < x \leq 2 π \end{cases}$

Step by Step Solution

Step 1.Given information

Step 2.Calculate some points for sinx in their given domain

Step 3.Calculate some points for cosx in their given domain

Step 4.Plot the above ordered pairs on the graph and connect them with a smooth curve.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problem 85 and 86 graph each of the functiong(x)=2sinx if 0≤x≤πcosx+1 ifπ<x≤2π

Step by Step Solution

Step 1.Given information

Step 2.Calculate some points for sinx in their given domain

Step 3.Calculate some points for cosx in their given domain

Step 4.Plot the above ordered pairs on the graph and connect them with a smooth curve.

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In Problem $85 a n d 86$ graph each of the function
$g (x) = \{\begin{cases} 2 \sin x i f 0 \leq x \leq π \\ \cos x + 1 i f π < x \leq 2 π \end{cases}$