Trig, how long is the graph under y=0

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In summary, the conversation discusses how to determine the duration of negative temperatures in a given function without using calculus. The suggested method involves setting the function equal to zero and finding the corresponding values of x. The use of a graphing calculator is not necessary, as the problem can be solved by analyzing the function.
  • #1
BadatPhysicsguy
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Homework Statement


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.

Homework Equations

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?
 
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  • #2
BadatPhysicsguy said:

Homework Statement


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.

Homework Equations

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?
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
BadatPhysicsguy said:

Homework Statement


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.

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.

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?

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.
 
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Related to Trig, how long is the graph under y=0

1. How do you plot a graph under y=0 for trig functions?

To plot a graph under y=0 for trig functions, you need to first identify the points where the function intersects with the x-axis. These points are known as the roots or zeros of the function. Once you have identified the roots, you can plot these points on the x-axis and then connect them with a smooth curve to create the graph under y=0.

2. What is the period of a trig function when graphed under y=0?

The period of a trig function when graphed under y=0 is the distance between two consecutive points where the graph intersects with the x-axis. It is the length of one complete cycle of the function. The period can be calculated by finding the difference between the x-values of two consecutive roots.

3. How do you determine the end points of a graph under y=0 for trig functions?

The end points of a graph under y=0 for trig functions can be determined by finding the maximum and minimum values of the function. These points are known as the amplitude points and they represent the highest and lowest points of the graph. The end points can also be found by extending the graph in both directions until it intersects with the x-axis.

4. Can the graph under y=0 for trig functions be symmetrical?

Yes, the graph under y=0 for trig functions can be symmetrical. This means that the graph will be identical on both sides of the y-axis. The degree of symmetry depends on the type of trig function and the values of its parameters. For example, the graph of y=sin(x) is symmetrical about the origin, while the graph of y=cos(x) is symmetrical about the y-axis.

5. How does the graph under y=0 for trig functions change with different values of the parameters?

The graph under y=0 for trig functions can change significantly with different values of the parameters. For example, changing the amplitude or frequency of a sine or cosine function can result in a taller or wider graph. Similarly, changing the phase shift or vertical shift of a trig function can shift the graph horizontally or vertically. It is important to understand how these parameters affect the graph in order to accurately plot and interpret it.

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