Question

In Buenos Aires , Argentina, the average monthly temperature is highest in January and lowest in July, ranging from 83 degrees to 57 degrees. Write a cosine function that models the change in temperature according to the month of the year.
How can you find the amplitude?
What part of the problem describes the length of the cycle?

Answer 1

The cosine itself goes from -1 to 1
If this is multiplied with an amplitude, then the cosine will go from -amplitude to +amplitude.

Answer 2

I don't get it still..

Answer 3

Hey,

the temperature should be modeled by a cosine function, so the shape of the temperatures will be round.
What we have to do is to get a cosine that at least resembles the actual data.

We can adjust the cosine function by changing the following properties:
- the amplitude, which is how much the function "lashes out"
- frequency, which is basically the number of turns per year

Answer 4

The amplitude is the distance from the x-line to an extreme. For a standard cosine function, the distance from x-line to the min and from x-line to the max are the same absolute value and that distance is called the amplitude.

Because the cosine function extends both into the positive and into the negative direction, the total distance from min to max is double the amplitude.

In our problem we are given min and max temperature, and we need an amplitude with which our modeled cosine will have the same reach as the temperature data (same distance from min to max).