Question

State the 5 reasons why the inverses of the 6 trig functions are chosen in the way they are."

For example, why is -pi/2 to pi/2 chosen for the inverse sin function. There are many other sections of the inverse sin graph that could have been chosen, so why this one?

Each of these reasons is explained in words. Do not separate and address the 6 trig inverses. You are looking at the whole picture. In fact, one or more of the reasons might not be true for one or more of the inverses. It is a general statement- with 5 reasons- that you want.

Answer 1

First conditions of inverse function is it must be one-one and onto function.

, so why we cut the range in be (-pi/2, pi/2)

1)) all trigonometric functions become one one function

2)) all become onto function

3)) for all the value of y there is only one pre image x,

4))its gives the principal value only

5)) for single value of x there is only single value of y , if not cut in between these domains then it has multiple value of y at Single x, or it's not no longer inverse function

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