Answer:
Explanation:
The general cosine wave function is:
y = A cos(ωt + φ) + B
where A is the amplitude, ω is the frequency, φ is the phase offset, and B is the vertical offset.
The temperature ranges from -10 to 50, so the magnitude of the amplitude is:
|A| = (50 − -10) / 2
|A| = 30
It's at its lowest point at t=0, so the sign of the amplitude is -1:
A = -30
The lowest point, -10, is 20 more than the amplitude, so the vertical offset is:
B = 20
The reaction completes 1 cycle in 6 hours, so f = 1/6. ω = 2πf, so:
ω = 2π (1/6)
ω = π/3
So the function is:
y = -30 cos(π/3 t) + 20
Alternatively, instead of a negative sign, we could have added a phase shift of π:
y = 30 cos(π/3 t + π) + 20
Either of these answers is correct.
