Answer:
1.7 seconds, and
3.3 seconds
Step-by-step explanation:
We simply need to plug in 8 into h and solve for t:
[tex]h=-15Cos(\frac{2\pi}{5}t)\\8=-15Cos(\frac{2\pi}{5}t)\\-\frac{8}{15}=Cos(\frac{2\pi}{5}t)\\\frac{2\pi}{5}t=Cos^{-1}(-\frac{8}{15})\\\frac{2\pi}{5}t=2.13\\t=\frac{2.13}{\frac{2\pi}{5}}\\t=1.70[/tex]
Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.
First, π - 2.13 radians = 1.01 radians.
Then, we add 1.01 to π radians, so we get 4.15 radians
Solving from the last part, we have:
[tex]t=\frac{4.15}{\frac{2\pi}{5}}\\t=3.3[/tex]
also, t = 3.30 seconds
*Note: we put the calculator mode in radians when solving
So, t = 1.7 seconds & 3.30 seconds
