Urgent: Sinusoidal functions HELP NOW PLZ

• Dec 9th 2008, 01:42 PM
jmac
Urgent: Sinusoidal functions HELP NOW PLZ
A boat tied up at a dock bobs up and down with the passing waves. The vertical distance between its high point and its low point is 1.8m and the cycle is repeated every 4s.

a.) Determine a sinusoidal equation to model the vertical position, in metres, of the boat vs. the time, in seconds.

I got this part of the equation and it is: y=.9sin(pi/2t)
but the second part i cant get.

b.) Use your equation to determine when, during each cycle, the boat is 0.5m above its mean position. Round your answers to the nearest hundreth of a second.

• Dec 9th 2008, 02:01 PM
skeeter
the easy way to do this is to graph $\displaystyle y = .5$ and $\displaystyle y = .9\sin\left(\frac{\pi}{2}t\right)$ and calculate the intersections.

here's the algebraic method (still need a calculator to get to the nearest hundredth of a second)

$\displaystyle .9\sin\left(\frac{\pi}{2}t\right) = .5$

$\displaystyle \sin\left(\frac{\pi}{2}t\right) = \frac{5}{9}$

$\displaystyle \frac{\pi}{2}t = \arcsin\left(\frac{5}{9}\right)$

$\displaystyle t = \frac{2}{\pi} \cdot \arcsin\left(\frac{5}{9}\right) \approx 0.37$

and ..

$\displaystyle t = \frac{2}{\pi} \cdot \left[\pi - \arcsin\left(\frac{5}{9}\right)\right] \approx 1.63$