Chapter 6: Q. 33 (page 410)

In Problems 31–34, match the given function to one of the graphs (A)– (D).
$y = 3 \sin (2 x)$

Short Answer

Expert verified

The graph of the given function is graph (B)

Step by step solution

Step 1. Given information

The trigonometric function is:

$y = 3 \sin (2 x)$

Step 2. To determine the amplitude and period of the sinusoidal function.

By comparing given function $3 \sin (2 x)$ with standard sinusoidal function $A \sin (ω x)$

We get amplitude $A = 3$

Time period is $T = \frac{2 π}{ω} T = \frac{2 π}{2} T = π$

So the graph of the given function will have time period $π$ and amplitude 3

Step 3. To find passing points of the graph

At y-axis

$x = 0$

then $y = 3 \sin (2.0) y = 3 \sin 0 y = 3.0 y = 0$

Graph will pass through (0,0)

when role="math" localid="1646496063332" $x = \frac{π}{4}$

$y = 3 \sin (2 . \frac{π}{4}) y = 3 \sin (\frac{π}{2}) y = 3.1 y = 3$

So the graph will pass through (0,0) and $(\frac{π}{4}, 3)$

Now look at the given graphs from A-D, we can see that

graph (B) has amplitude 3 , time period $π$ and passing point (0,0) and $(\frac{π}{4}, 3)$

So the graph for given function is graph (B)

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In Problems 31–34, match the given function to one of the graphs (A)– (D).
$y = 3 \sin (2 x)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. To determine the amplitude and period of the sinusoidal function.

Step 3. To find passing points of the graph

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In Problems 31–34, match the given function to one of the graphs (A)– (D).y=3sin2x

Short Answer

Step by step solution

Step 1. Given information

Step 2. To determine the amplitude and period of the sinusoidal function.

Step 3. To find passing points of the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 31–34, match the given function to one of the graphs (A)– (D).
$y = 3 \sin (2 x)$