finding the average in a a cosine graph.
would the average be the the middle of the y-axis for the graph?
for example, for y = cos x
would the average be 0
To find the average of a cosine graph, you need to find the average value of the y-coordinate over a specific interval.
For the graph of y = cos(x), the average value would not be the middle of the y-axis (0). This is because the graph of cosine oscillates above and below the x-axis.
To find the average value, you can use the following formula:
Average value = (1 / (b - a)) * ∫[a, b] cos(x) dx
where [a, b] represents the specific interval over which you want to find the average.
For example, if you want to find the average value of y = cos(x) over the interval [0, 2π], you would use the following integral:
Average value = (1 / (2π - 0)) * ∫[0, 2π] cos(x) dx
After evaluating this integral, you would find that the average value of y = cos(x) over the interval [0, 2π] is 0.
So, in this particular case, the average value of the cosine graph y = cos(x) is indeed 0 over the interval [0, 2π].