Isabella is playing with her yo-yo. The vertical distance YY
Y
Y
(in
cm\text{cm}
cm
start text, c, m, end text
) between the yo-yo and her hand
tt
t
t
seconds after she first spins it out is modeled by the following function. Here,
tt
t
t
is entered in radians.
Y(t)=40cos⁡(2π3t)−71Y(t) = {40}\cos\left({\dfrac{2\pi}{3}}t\ri ght) - {71}
Y(t)=40cos(
3

2π


t)−71
Y, left parenthesis, t, right parenthesis, equals, 40, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 71
How long does it take the yo-yo to fall all the way down from its peak, and then rise up to a vertical distance of
−80 cm-80\text{ cm}
−80 cm
minus, 80, start text, space, c, m, end text
?
Round your final answer to the nearest tenth of a second.