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umka21 [38]
3 years ago
10

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!

Mathematics
1 answer:
lianna [129]3 years ago
7 0
Let us consider the function given. It is y=cos \frac{1}{2}x. 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=2 \pi. Put another way, to see a full cycle we would need \frac{2 \pi }{ \frac{1}{2} }=4 \pi. The period of the function given is 4 \pi.

Let us think about a cycle of cosine. It starts (x=0) and ends (x=4 \pi) its cycle at its highest value (here f(x)=1). It is at it's lowest (here f(x)=-1) in the middle (x=2 \pi) it is between the highest and the lowest that it crosses the x-axis.

That is, it has an x-intercept between 0 and 2 \pi That is, at \pi

The next one comes between 2 \pi and 4 \pi. That is, at 3 \pi

The attached shows the function and it's x-intercepts. You can see that they occur at: \pi ,3 \pi ,5 \pi ,7 \pi ,9 \pi ,.... This is the arithmetic sequence that contains the x-intercepts of the function.

As you can see the nth zero will occur at n \pi


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