For a cosine function with amplitude A=0.75 and period T=10, what is y(4)?
2π/T = 2π/10 = π/5
y(x) = A sin (wx) = 0.75 sin (πx/5)
y(4) = 0.75 sin (4π/5) = 0.4408389392... ≈ 0.441
Answer:
y(4) = -0.606
Explanation:
Given that,
The amplitude of cosine function, A = 0.75
Time period, T = 10
The cosine function is given by :
\(y=A\ cos(\omega t)\)
Since, \(\omega=\dfrac{2\pi}{T}\)
\(y=A\ cos(\dfrac{2\pi}{T}t)\)
\(y=0.75\ cos(\dfrac{2\pi}{10}t)\)
We need to find y (4). Put t = 4 in above equation as :
\(y(4)=0.75\ cos(\dfrac{2\pi}{10}\times 4)\)
y(4) = -0.606
Hence, this is the required solution.