Verified Answer :

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 \((\frac{-\pi}{2} ,-1)\) is a relative maximum and

\((\frac{\pi}{2} ,1)\) is a relative minimum.

Vertical lines are asymptotes of the graph i.e, \(x = n\pi\)

Period =  \(2\pi\)

Domain of the function y= csc s is: All x ≠\(n\pi\)

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

* Symmetry:  Origin


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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 \(\theta\) is given by:

\(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}\)

  • The cotangent is given by:

\(\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}\)

The secant is given by:

\(\sec{\theta} = \frac{1}{\cos{\theta}}\)

The cosecant is given by:

\(\csc{\theta} = \frac{1}{\sin{\theta}}\)

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

At \(x = \frac{\pi}{4} \approx 0.785\), we have that \(y eq 1\), which means that the function is the cosecant, as:

\(\cot{\frac{\pi}{4}} = \frac{\cos{\frac{\pi}{4}}}{\sin{\frac{\pi}{4}}} = 1\)

\(\csc{\theta} = \frac{1}{\sin{\theta}} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}\)

Hence, option D is correct.

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

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