Question

Business. Computer sales are generally subject to seasonal fluctuations. An analysis of the sales of a computer manufacturer during 2015-2017 is approximated by the function

s (t) = 0.082 cos, + 0.393 1 < t < 12
where t represents time in quarters (t = 1 represents the end of the first quarter of 2015), and s (t) represents computer sales (quarterly revenue) in millions of dollars. Use a double-angle identity to express s (t) in terms of the cosine function
Enclose arguments of functions in parentheses. For example, sin (2x)
s(t) = __________

Answer 1

The expression of s(t) using double-angle identity is

`s(t) = 0.434 + 0.041 cos (2t)`

Explanation:

From the question we are told that

The sales of a computer manufacturer during 2015-2017 is approximated by the function

`s(t) = 0.082cos^2(t) + 0.393 \ \ \ \ 1 \le t \le 12`

Now applying the double-angle to express s (t) in terms of the cosine function we have

`s(t) = 0.082 [(1 + cos(2t))/(2) ] + 0.3931` Note that
`cos^2t = (1 + cos(2t))/(2)`

`s(t) = (0.082)/(2) [1 + cos(2t) ] + 0.393`

`s(t) = 0.041 [1 + cos(2t) ] + 0.393`

`s(t) = 0.041 + 0.041 * cos(2t) + 0.393`

`s(t) = 0.434 + 0.041 cos (2t)`