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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!

Respuesta :

Thagie
Let us consider the function given. It is [tex]y=cos \frac{1}{2}x [/tex]. 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=[tex]2 \pi [/tex]. Put another way, to see a full cycle we would need [tex] \frac{2 \pi }{ \frac{1}{2} }=4 \pi [/tex]. The period of the function given is [tex]4 \pi [/tex].

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

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

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

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

As you can see the nth zero will occur at [tex]n \pi [/tex]


Ver imagen Thagie

The arithmetic sequence of the cosine function is given as π, 3π, 5π, 7π, 9π, ..... or nπ.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The arithmetic sequence that gives the nth positive x-intercept of the graph of a function is given below.

[tex]f(x)=\cos\dfrac{1}{2}x[/tex]

The frequency of the curve is given by the coefficient of x. This indicates that between x = 0 and x = 2π, we witness 1/2 of a cycle.

The period of the provided function is 4π.

Consider the case of a cosine cycle. It begins (x = 0) and finishes (x = 4π) its cycle at its maximum value (f(x) = 1). It has reached its lowest point (f(x) = - 1). It crosses the x-axis in the center (x = 2π), between the highest and lowest points.

Its x-intercept ranges from 0 to 2π. That is to say, at π.

Between 2π and 4π is the following one. At 3π

Then the arithmetic sequence will be given as

π, 3π, 5π, 7π, 9π, .....

As you can see the nth zero will occur at nπ.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

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