SOLUTION: Write the equation sin y=x in the form of an inverse function. Thank you

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Question 42390: Write the equation sin y=x in the form of an inverse function.
Thank you

Found 2 solutions by fractalier, AnlytcPhil:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
If you take the inverse sin of both sides you get
sin y = x
sin^(-1) sin y = sin^(-1) x
y = sin^(-1) x

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation sin(y) = x in the form of an inverse function.

Thank you

The equation in words would be

"The sine of y is x"

That sentence can be written this way:

"y is what we must take the sine of to get x"

The mathematical symbol for the words

"what we must take the sine of to get"

is 

sin-1

That is not really a "negative one exponent", it's
only written that way because a negative
one exponent is what inverts a fraction, and that 
reminds us that we are writing another kind of 
inverse somewhat analogous to that, but far from
meaning that.

So from the beginning:

sin(y) = x

translates as

"The sine of y is x"

which translates as 

"y is what we have to take the sine of to get x"

which translates as

y = sin-1(x)

Edwin
AnlytcPhil@aol.com