Help finding max and min of cosine function please. Question attached. I used wolfram alpha to verify the answer, I get the first part, but not the second.

Question

azureilai · Answer

The max comes out to be 6.2 + 12.4n, and the min = 12.4 n. I got the 6.2 part, but I have no idea where the 12.4 comes from

anonymous · Answer

the maximum value of cosine is 1 and the minimum is -1
the maximum values of $-28\cos(x)$ is $28$ and the minimum value is $-28$

anonymous · Answer

are you trying to find the maximum and minimum, or the $t$ that gives it?

azureilai · Answer

im trying to find the t that gives it

azureilai · Answer

this is my work so far, not sure if I did it correct

anonymous · Answer

max is when cosine is $-1$ which will give you $35+28=63$'
that occurs when $\frac{\pi}{6.2}t=\pi$

anonymous · Answer

solve in one step, get $t=\frac{6.2}{\pi}\times \pi=6.2$

anonymous · Answer

and of course min occurs when $t=0$

azureilai · Answer

yes, I got that, but since it is periodical, wolfram said max occurs at 6.2+12.4n for max, and 12.4n for min. I am wondering where the 12.4 came from.

anonymous · Answer

just as you said, it is periodic 
well not "periodical" but you have the right idea
so max occurs if $\frac{\pi}{6.2}=\pi,3\pi,5\pi,...$

anonymous · Answer

the first one gives $t=6.2$ the second one gives $3\times 6.2$ etc

azureilai · Answer

ok I see thank you for your help.

anonymous · Answer

notice that wolfram has for the max $6.2+12.4n$ which is the same thing
yw