The curve above the graph of a sinusoidal function. It goes through the points (-11,0) and (3,0). Find a sinusoidal function that matches the given graph.if needed you can enter pi=3.1416… as pi in your answer otherwise use at least 3 decimal digits.
F(x)=

Considering the zeros, the graph for the sinusoidal function is:

[tex]F(x) = \sin{\frac{\pi}{7}(x-3)}[/tex]

The sine function is given by:

[tex]F(x) = A\sin{Bx}[/tex]

In which:

In this problem:

[tex]\frac{2\pi}{B} = 14[/tex]

[tex]B = \frac{2\pi}{14}[/tex]

[tex]B = \frac{\pi}{7}[/tex]

Thus:

[tex]F(x) = \sin{\frac{\pi}{7}x}[/tex]

Like this, the zeros are at [tex]x = -14[/tex] and [tex]x = 0[/tex]. We want it at [tex]x = -11, x = 3[/tex], thus, we shift the function 3 units to the right, that is, the function is:

[tex]F(x) = \sin{\frac{\pi}{7}(x-3)}[/tex]

The graph is sketched at the end of this answer, and has the desired behavior, which are points (-11,0) and (3,0).

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