# Homework Help: Trig, how long is the graph under y=0

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1. Nov 6, 2014

1. The problem statement, all variables and given/known data
f(x)=20+25*sin(0.85x)
x = number of hours from start. f(x) = temperature.
For how long is the temperature negative (under 0) during the first 10 hours? We haven't learned how to derive/integrate trig equations so that is out of the question.

2. Relevant equations

3. The attempt at a solution
Most people with similar problems have said they used their graph calculator to solve these kinds of questions. I tried figuring out the period (7.39) and took the half of that + the remaining 2.61 but during those there is no more under the graph. So the answer would seem to be around 3.7 but it is only 1.5. How do I use my graph calculator (TI-84) to solve this?

2. Nov 6, 2014

### Staff: Mentor

You could set f(x) = 0 and solve the resulting equation. There are two values of x in the interval 0 ≤ x ≤ 10 for which f(x) = 0. Find these values and you'll have the interval where the temperature is negative.

3. Nov 6, 2014

### SteamKing

Staff Emeritus
You don't need calculus to solve this problem. You just need to find out for 0≤x≤10 where f(x) < 0. You can use a little algebra to clean things up a bit.

Instead of using your calculator to think for you, try working the problem out by analyzing it. You're not going to school to learn how to work a calculator, but how to learn to analyze and solve problems.

4. Nov 6, 2014