trigonometry - Fitting data with Cosine

So I'm trying to wrap my head about Graphing Cos and Sin but I have several questions about graphing. I know that the Formula is

$$Y= A \sin (t \pm h) + K$$

where $A$ is Amplitude , $t$ is Period, $h$ is horizontal shift, $k$ is the mid line.

I have the following data...

I know for fact the following...

Highest Point $= 73$

Lowest point $= 43$

Amplitude $= (73 - 43) = 30$

Midline $= (A/2 + 43) = 30/2 + 43 = 58$

Now the problem is putting all the information together...

$y = 15 \cos (t \pm h) + 58$

my question is figuring the Period and Horizontal shift?

I think $t$ (period), is the number of cycles between $0$ and $24$ so it's $24/1$

$t= 24/1 = 24$

but the graph shrinks?

I'm having trouble understanding how to obtain t- period and h- horizontal shift.

Most of the graphs on the internet use $2\pi/$(# of intervals).