Write an arithmetic sequence that gives the nth positive x-intercept of the graph of f(x)=cos1/2x. leave your answer in terms of π. will give brainliest!

Let us consider the function given. It is . The coefficient of x (here 1/2) gives the frequency of the curve. What this means is that we see 1/2 a cycle between x=0 and x=. Put another way, to see a full cycle we would need . The period of the function given is .

Let us think about a cycle of cosine. It starts (x=0) and ends () its cycle at its highest value (here f(x)=1). It is at it's lowest (here f(x)=-1) in the middle () it is between the highest and the lowest that it crosses the x-axis.

That is, it has an x-intercept between 0 and That is, at

The next one comes between and . That is, at

The attached shows the function and it's x-intercepts. You can see that they occur at: . This is the arithmetic sequence that contains the x-intercepts of the function.

As you can see the nth zero will occur at