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Answer:
The domain window setting that would be appropriate to graph the function is;
[tex]x_{min}[/tex] = -90°, [tex]x_{max}[/tex] = 270°
Step-by-step explanation:
The given equation is y = 4·sin(3·x)
We note that one period of the sine function = 2·π = 360°
Therefore, if we wanted to graph the above function for exactly three periods, then we should have;
The domain of the function will be from 0 to 3 × 360
Minimum value of 3·x = 0,
Maximum value of 3·x= 3 × 360°
Therefore;
Minimum value of x = 0°/3 = 0° and maximum value of x = 3 × 360°/3 = 360°
Which gives the extent of the domain as 360°
The appropriate domain window setting to graph the function therefore, [tex]x_{min}[/tex] = -90°, [tex]x_{max}[/tex] = 270° as the extent is 270 - (-90) = 360°
The domain window setting is the minimum and maximum x-values of a function.
The appropriate domain window settings are: [tex]X_{min} = -90[/tex] and [tex]X_{max} = 270[/tex]
We have:
[tex]y = 4\sin(3x)[/tex]
A sine function is represented as:
[tex]y = A(\sin(B(x + C))[/tex]
Where:
[tex]B \to[/tex] period
By comparing [tex]y = A(\sin(B(x + C))[/tex] and [tex]y = 4\sin(3x)[/tex]
We have the value of B to be: [tex]B = 3[/tex]
For a sine function, the value of 1 period (T) is:
[tex]T = 2\pi[/tex]
Convert to degrees
[tex]T = 2 \times 180^o[/tex]
[tex]T = 360^o[/tex]
The difference between the domain window settings is then calculated as follows:
[tex]X_{max} - X_{min}= B \times \frac{T}{3}[/tex]
So, we have:
[tex]X_{max} - X_{min}= 3 \times \frac{360^o}{3}[/tex]
[tex]X_{max} - X_{min}= 360^o[/tex]
This means that the difference between the window settings must be [tex]360^o[/tex]
The option that satisfies this condition is:
(a) [tex]X_{min} = -90[/tex] and [tex]X_{max} = 270[/tex]
This is so, because:
[tex]X_{max} - X_{min}= 360^o[/tex]
Substitute [tex]X_{min} = -90[/tex] and [tex]X_{max} = 270[/tex]
[tex]270^o - (-90^o) = 360^o[/tex]
Open brackets
[tex]270^o + 90^o = 360^o[/tex]
[tex]360^o = 360^o[/tex]
Hence, the appropriate domain window settings are:
[tex]X_{min} = -90[/tex] and [tex]X_{max} = 270[/tex]
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