Question

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

Answer 1

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

Answer 2

We need to find a cosine function:

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

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:

$a=0.75 \\ \\ b=\frac{2\pi}{10}=\frac{\pi}{5}$

Finally:

$\boxed{y(x)=0.75cos(\frac{\pi}{5}x)}$

And y(4) is:

$y(4)=0.75cos(\frac{\pi}{5}\times 4) \\ \\ \therefore \boxed{y(4)=-0.60}$