Question

The number of daylight hours on a given day of the year, t, in Cleveland, Ohio, is given by the function

f(x) = 3 sin (35t-1.34) +9.5
What is the least number of hours of daylight in Cleveland, Ohio?
What is the greatest number of hours of daylight in Cleveland, Ohio?

Answer 1

• least: 6.5 hours
• most: 12.5 hours

Explanation:

You want to know the least and most number of daylight hours if the function f(t) = 3·sin(35t -1.34) +9.5 gives the number of daylight hours.

Sine

The sine function has a minimum of -1, and a maximum of +1. The value of f(t) will be minimum or maximum at these extreme values of the sine function.

minimum: f(t) = 3(-1) +9.5 = 6.5

maximum: f(t) = 3(+1) +9.5 = 12.5

The least number of hours of daylight is 6.5 in Cleveland; the greatest number is 12.5.

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