For a sine function with amplitude =0.75 and period =10 , what is y(4) ?

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For a sine function with amplitude =0.75 and period =10 , what is y(4) ?

We need to find a cosine function:

[tex]y(x)=acos(bx) \\ \\ where: \\ \\ \left|a\right|=Amplitude \\ \\ Period=\frac{2\pi}{b}[/tex]

The amplitude represents half the distance between the maximum and minimum values of the function and the period goes from the x-value of one peak to the x-value of the next one. Therefore:

[tex]a=0.75 \\ \\ b=\frac{2\pi}{10}=\frac{\pi}{5}[/tex]

Finally:

[tex]\boxed{y(x)=0.75cos(\frac{\pi}{5}x)}[/tex]

And y(4) is:

[tex]y(4)=0.75cos(\frac{\pi}{5}\times 4) \\ \\ \therefore \boxed{y(4)=-0.60}[/tex]

From my research, the cosine function is:

y(t) = Acos(ωt)

Where:

A = amplitude = 0.75

ω = angular velocity = (2*pi)/T = (2*pi)/10 = 0.6283

Therefore:

y(4) = 0.75*cos(0.6283*4)

y(4) = 0.61

The general formula for sine function is y(x) = A sin(2πx/t). Here, x = displacement = 4 , time period , t = 10 and Amplitude, A = 0.75, then, y(4) = 0.75 sin( 2π*4/10) = 0.75*0.04 =0.03. Thus, the value of y(4) wll be 0.03