# Question #c5c0e

Jun 17, 2015

Have a look if it makes sense:
$H \left(t\right) = 10 - 7 \cos \left(\frac{\pi}{10} t\right)$

#### Explanation:

Your sinusoidal function oscillates between $17$ and $3$ so its amplitude must be:
$A = \frac{17 - 3}{2} = 7 f t$
The period of your function is 20 seconds (after which it repeats itself); for this reason the $t$ in the argument must be multiplied by $\frac{2 \pi}{p e r i o d} = \frac{\pi}{10} {\sec}^{-} 1$;
Your function seems a cosine but starting from the negative and shifted up of 10 feet.
I would write it as:
height: $H \left(t\right) = 10 - 7 \cos \left(\frac{\pi}{10} t\right)$
Graphically:
graph{10-7cos((pi/10)*x) [-52, 52.04, -26, 26.03]}

Jun 17, 2015

y= 7sin $\frac{\pi}{10} \left(t - 5\right)$ +10

#### Explanation:

The equation can also be written in terms of sine function. From the graph the horizontal shift can be noted to be 5 units, amplitude being 7, vertical shift being 10, the sinusoidal function would be y= 7 sin $\frac{\pi}{10} \left(t - 5\right)$ + 10