Question

Question #c5c0e

Answer 1

Have a look if it makes sense:
`H(t)=10-7cos(pi/10t)`

Explanation:

Your sinusoidal function oscillates between `17` and `3` so its amplitude must be:
`A=(17-3)/2=7ft`
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 `(2pi)/(period)=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(t)=10-7cos(pi/10t)`
Graphically:
graph{10-7cos((pi/10)*x) [-52, 52.04, -26, 26.03]}

Answer 2

y= 7sin `pi/10(t-5)` +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 `pi/10(t-5)` + 10