A ship is docked in port and rises and falls with the waves.
The model h(t)=sin(PI/5)t describes the vertical movement of the ship, h, in metres at t seconds

What is the period of the function?
Determine all the times within the first minute that the vertical position of the ship is -0.9m to the nearest tenth of a second.

I'm not sure as to how im supposed to figure these out. Am i supposed to actually draw the graph to represent this or something?

2. Originally Posted by sugar_babee
A ship is docked in port and rises and falls with the waves.
The model h(t)=sin(PI/5)t describes the vertical movement of the ship, h, in metres at t seconds

What is the period of the function?
Determine all the times within the first minute that the vertical position of the ship is -0.9m to the nearest tenth of a second.

I'm not sure as to how im supposed to figure these out. Am i supposed to actually draw the graph to represent this or something?
The period is $\displaystyle 2\pi$ divide by the frequency $\displaystyle \pi /5$ Thus,
$\displaystyle \frac{2\pi}{1}\cdot \frac{5}{\pi }=10$

For the second part you need to solve,
$\displaystyle \sin(\pi /5 x)=-.9$

3. How do i isolate the PI from the 5x? do i just multiply each side by it, or is there something more to it?

4. Originally Posted by sugar_babee
How do i isolate the PI from the 5x? do i just multiply each side by it, or is there something more to it?
No, you used take the inverse sine, thus,
$\displaystyle \frac{\pi}{5}x=\sin^{-1}(-.9)$
Thus,
$\displaystyle x=\frac{5}{\pi}\sin^{-1}(-.9)$