Stewart's ET Calculus book 6E. An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled down and then released, it vibrates vertically. The equation of motion, s, where s is measured in centimeters and t≥0 in seconds, is given below. (Take the positive direction to be downward.)

s = 8 cos (t) + 4 sin (t)

I found velocity and acceleration
v(t)= -8sin(t) +4cos(t)
a(t)= -8cos(t) - 4sin(t)

MY problem comes in the question c
(c) When does the mass pass through the equilibrium position for the first time?
I tired 8 cost + 4 sint =0 getting tan inverse of -8/4. then π+tan inverse of -8/4 which lead me to the answer 1.82?

My second problem comes with question d

d) How far from its equilibrium position does the mass travel?