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=(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=(2\pi)/(10)=(\pi)/(5)`

Finally:

`\boxed{y(x)=0.75cos((\pi)/(5)x)}`

And y(4) is:

`y(4)=0.75cos((\pi)/(5)* 4) \\ \\ \therefore \boxed{y(4)=-0.60}`