Respuesta :

Answer:

Option D is correct.

The function whose graph is given is y = csc x

Step-by-step explanation:

The function whose graph is shown below in the graph is y = csc x

if we look the graph we observe that [tex](\frac{-\pi}{2} ,-1)[/tex] is a relative maximum and

[tex](\frac{\pi}{2} ,1)[/tex] is a relative minimum.

*Vertical lines are asymptotes of the graph i.e, [tex]x = n\pi[/tex]

* Period =  [tex]2\pi[/tex]

* Domain of the function y= csc s is: All x ≠[tex]n\pi[/tex]

*Range: [tex](-\infty , 1]\cup[1, \infty)[/tex]

* Symmetry:  Origin


Ver imagen OrethaWilkison

Using trigonometric function concepts, it is found that the function defined on the graph is:

D. y = csc x

What is the tangent, cotangent, secant and cosecant of an angle?

  • The tangent of an angle [tex]\theta[/tex] is given by:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

  • The cotangent is given by:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The secant is given by:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}}[/tex]

The cosecant is given by:

[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]

In this problem, the discontinuities are at [tex]\pm k\pi, k = 0, 1, 2, \cdots[/tex], which implies that the term at the denominator is a sine.

At [tex]x = \frac{\pi}{4} \approx 0.785[/tex], we have that [tex]y \neq 1[/tex], which means that the function is the cosecant, as:

[tex]\cot{\frac{\pi}{4}} = \frac{\cos{\frac{\pi}{4}}}{\sin{\frac{\pi}{4}}} = 1[/tex]

[tex]\csc{\theta} = \frac{1}{\sin{\theta}} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}[/tex]

Hence, option D is correct.

You can learn more about trigonometric functions at https://brainly.com/question/18055768

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