Answer: It is y=sin^-1(1/x)
Step-by-step explanation: that is the right answer on edge
The trigonometric function gives the ratio of different sides of a right-angle triangle. The graph y = y =csc⁻¹(x) on the calculator can be written as y=sin⁻¹(1/x).
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.
As the function that is given to us is y = csc⁻¹(x), therefore, the function can be rewritten as,
[tex]y=cosec^{-1}x\\cosec\ y = x[/tex]
Since sin is the inverse of cosec, therefore, the function can be written as,
[tex]sin\ y= \dfrac{1}{cosec\ y}\\\\\text{Substitute the value of cosec(y)}\\\\sin\ y=\dfrac{1}{x}\\\\y = sin^{-1}\dfrac1x[/tex]
Thus, the graph y = y =csc⁻¹(x) on the calculator can be written as y=sin⁻¹(1/x).
Learn more about Trigonometric functions:
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