Can someone help me solve this problem?

[randall weidner]

Could someone help me out with how to solve this problem. Thank you in advance.

[annales2maths]

a. As

$mathjax$s(0) = 1$mathjax$

and

$mathjax$s(0) = a \cos(0 \times \omega) = a$mathjax$

then we can find the value of

$mathjax$a$mathjax$

We also know that the period is

$mathjax$P=1.1$mathjax$

that means that for all

$mathjax$x,$mathjax$

$mathjax$s(x+P)= s(x)$mathjax$

. Therefore

$mathjax$a \cos\left(\omega x + \omega \times P\right) = a\cos(\omega x)$mathjax$

.
But the period of the cosine function is

$mathjax$2\Pi$mathjax$

. So

$mathjax$\omega P = 2\Pi$mathjax$

. That will give you the value of

$mathjax$\omega$mathjax$

b. You just have now to evaluate your function with the value of

$mathjax$a$mathjax$

and

$mathjax$\omega$mathjax$

found at the previous question.

c. Use your calculator to sketch the curve of your function and look around

$mathjax$t=1$mathjax$