Thread: Sinusoidal Functions-word problem

1. Sinusoidal Functions-word problem

I really need help on this problem:

A rodeo performer spins a lasso in a circle perpendicular to the ground. The height of the knot from the ground is modeled by h= -3 cos (5 pi/3 t) +3.5, where t is the time measured in seconds.

a. What's the highest point reached by the knot
b. Lowest point reached by the knot
c. the period of the model
d. According to the model, find the height of the knot after 25 seconds.

2. $\displaystyle h=-3cos(\frac{5\pi}{3}t)+3,5$
a) the highest point reached by the knot is the maximum of this function:
$\displaystyle cos(\frac{5\pi}{3}t) \in <-1,1>$
$\displaystyle -3cos(\frac{5\pi}{3}t) \in <-3,3>$
$\displaystyle -3cos(\frac{5\pi}{3}t)+3,5 \in <0,5;6,5>$
the highest value we can get is $\displaystyle h=6,5$
b) and the lowest $\displaystyle h=0,5$
c) cosine function $\displaystyle cos t$ is periodic with period $\displaystyle 2\pi$, so $\displaystyle cos(\frac{5\pi}{3}t)$ is periodic with period $\displaystyle \frac{2\pi}{\frac{5\pi}{3}}=\frac{6}{5}$
d) $\displaystyle t=25$
$\displaystyle h=-3cos (\frac{5\pi}{3}*25)+3,5=-3cos (\frac{125\pi}{3})+3,5=$$\displaystyle -3cos(\frac{5\pi}{3})+3,5$
converting into degrees $\displaystyle \frac{5*180^o}{3}=300^o$
$\displaystyle h=-3cos(270^o+30^o)+3,5=-3*\frac{1}{2}+3,5=2$

3. Thanks