Question

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

Answer 1

 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 2

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.