let h(t)=4+4sin(pit/2). approximate to the nearest hundredth, all values t in the interval [0,4pi] for which h

Question

let h(t)=4+4sin(pit/2). approximate to the nearest hundredth, all values t in the interval [0,4pi] for which h(t)=6

which h(t)=6

Answer 1

h(t)=4+4sin(pit/2) =6
4sin(pit/2) =2
sin (pi t/2) = 1/2
then pi t/2 = pi/6
so t/2 = 1/6
and t = 1/3 which is about 0.33

Answer 2

Build a table:

t pi*t/2 sin(pi*t/2) 4+4*sin(pi*t/2)

(the last column is h)

You did not give us the condition on h.

I suspect that you are given conditions such as "for which h is between this value and that"

find the inverse function

h(t)=4+4sin(pit/2)
sin(pi*t/2) = (h - 4)/4

pi*t/2 = arcsin[(h-4)/4]
t = (2/pi)*arcsin[(h-4)/4]

where t is now a function of h
this will be a start.