Question

Describe the relationship between the domain of an inverse sine function and the range of a sine function

Answer 1

The answer is that they are both equal.

Explanation:

Answer 2

Answer: The answer is both are same.

Step-by-step explanation: We are given to describe the relationship between the domain of an inverse sine function and the range of a sine function.

Let

`y=\sin x~~\Rightarrow x=\sin^(-1)y.`

We know from Trigonometry that the domain and range of sine function are

`Domain~~~~~~~~~~~~~~~~~~~~~~~~~(-\infty< x<\infty)\\\\Range~~~~~~~~~~~~~~~~~~~~~~~~~~~~(-1\leq y\leq 1).`

Also, the domain and range of inverse sine function is given by

`Domain~~~~~~~~~~~~~~~~~~~~~~~~~(-1\leq y\leq 1)\\\\Range~~~~~~~~~~~~~~~~~~~~~~~~~~~~(-(\pi)/(2)\leq y\leq (\pi)/(2)).`

See the attached figures for more understanding.

Thus, it is clear from the explanation that the range of sine function and the domain of inverse sine function are same and it is equal to [-1, 1]