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raketka [301]
3 years ago
11

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

Mathematics
2 answers:
Westkost [7]3 years ago
8 0

Answer:

The answer is that they are both equal.

Step-by-step explanation:

Ne4ueva [31]3 years ago
5 0

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

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

Domain~~~~~~~~~~~~~~~~~~~~~~~~~(-1\leq y\leq 1)\\\\Range~~~~~~~~~~~~~~~~~~~~~~~~~~~~(-\dfrac{\pi}{2}\leq y\leq \dfrac{\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]


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