The function given represents the temperature of a sauna set to 180°F. The temperature goes up and down throughout the day. Find the period: 30 Find how many times the function reaches a maximum temperature in one hour: 180 f(x)=5sin(π15x)+180, where x is measured in minutes, and f(x) is measured in degrees Fahrenheit.

The answer is below

Step-by-step explanation:

Given the function as:

f(x)=5sin(πx / 15)+180,

a) The angular frequency (ω) = 2π * frequency

but ω = π/15, hence:

π/15 = 2π * frequency

frequency = (π/15)/2π

frequency = 1/30 hertz

Period (T) = 1/frequency = 1/(1/30) = 30 seconds

b) The period is 30 seconds. This means that it reaches the maximum temperature every 30 seconds.

In one hour (3600 s), the number of times the function reaches a maximum temperature = 3600 s / 30 s = 120