All information that was given to me is what is shown, Please quickly explain th

Question

All information that was given to me is what is shown, Please quickly explain the answers. Thank you.

This problem is about the inverse sine function, the reverse process of f(x) = sin x, which is denoted sin^-1 x, or arcsin x. (For this problem, f^-1 will also be used.) In the reverse process of f(x) = sin x, what are meanings of the input and output quantities? In the reverse process of f, what is the domain, i.e. all valid values of the input quantity of f^-1 that you identified in part a)? Which piece of the graph f(x) = sin x shows exactly one output of f^-1 for every input of f^-1? Based on your answer to part e), what is the range of f^-1 (x) =sin^-1 x, i.e. all possible outputs of the inverse sine function?

Explanation / Answer

y =sin^-1(x)

x is the input which is the y coordinate of the unit circle i.e. 1*sin(theta)

y is the output which is the angle swept counterclockwise

The range of sin(theta) varies between +1 and -1

Since sin^-1(x) is the inverse of sin(theta) so ist ragen becomes sin^-1(x) functions Domain.

Domain [-1 ,1 ]

e) Graph (E) shows one output for all inputs for sin^-1(x)

f) Based on part( e) , domain in graph E is the range of sin^-1(x)

We can see the domain fo graph E is -1.5<=x<=1.5 .This is the range of sin^-1(x)

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