Chapter 6: Q. 36 (page 410)

In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function
$y = 3 \sin x$

Short Answer

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Step by step solution

Step 1. Given information

The function to be plotted is

$y = 3 \sin x$

Step 2. Determine the amplitude and period of the sinusoidal function

Comparing $y = 3 \sin x$ to $y = A \sin (ω x)$ ,

We get $A = 3$ and v = p 2 . The amplitude is 3,

and the period is $T = \frac{2 π}{ω} T = \frac{2 π}{1} T = 2 π$

So. the graph of lies between -3 and 3 on the y-axis. One cycle begins at

x = 0

and ends at

x = 2 π

Step 2. Divide the interval 0,2π into four subintervals of the same length.

Divide the interval $[0, 2 π]$ into four subintervals, each of length $2 π \div 4 = \frac{π}{2}$

The x-coordinates of the five key points are

First x-coordinate is $0$

Second x-coordinate is $0 + \frac{π}{2} = \frac{π}{2}$

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In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function
$y = 3 \sin x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the amplitude and period of the sinusoidal function

Step 2. Divide the interval 0,2π into four subintervals of the same length.

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In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each functiony=3sinx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the amplitude and period of the sinusoidal function

Step 2. Divide the interval 0,2π into four subintervals of the same length.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Geometry

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function
$y = 3 \sin x$