Answer:
- Minimum and maximum temperatures are \(-30,100\)
- Time taken to complete one complete cycle is 10 hours.
Step-by-step explanation:
The general sinusoidal periodic function is,
\(f(t)=a\sin (b(t+c))+d\)
here,
- amplitude = a,
- period = \(\dfrac{2\pi}{b}\),
- horizontal or phase shift = c,
- vertical shift = d,
Comparing this with the given function \(f(t)=65\sin\dfrac{\pi}{5}x+35\), we get
- amplitude = a = 65,
- period = \(\dfrac{2\pi}{\frac{\pi}{5}}\) = 10,
- vertical shift = d = 35, so the axis of symmetry will be, \(y=35\)
The maximum and minimum temperatures will be,
\(=35\pm 65\)
\(=-30,100\)
Time taken to complete one complete cycle is the period, so it is 10 hours.
