Answer:
t = 0.77
Step-by-step explanation:
D(t) = 50 - 23 sin(π(t + 0.23))
The value of the sine function has a maximum of -1 and a minimum of 1.
The average value of the sine function is 0.
At maximum sine value:
D(t) = 50 - 23(1) = 50 - 23 = 27
At minimum sine value:
D(t) = 50 - 23(-1) = 50 + 23 = 73
At average sine value of 0:
D(t) = 50 - 23(0) = 50 - 0 = 50
The average depth of the waves is 50 cm.
Now we need to find at what time, t, that occurs.
D(t) = 50 - 23 sin(π(t + 0.23)) = 50
50 - 23 sin(π(t + 0.23)) = 50
-23 sin(π(t + 0.23)) = 0
sin(π(t + 0.23)) = 0
The value of the sine is 0 at 0, π, 2π, ..., nπ
π(t + 0.23) = nπ
t + 0.23 = n
t = n - 0.23
n is all integers, but here we are concerned with the first occurrence after time equals zero, so we want n = 1.
t = 1 - 0.23
t = 0.77
