Question 42390
<pre><font size = 4><b>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 <font color = "red">what we must take the sine of to get</font> x"

The mathematical symbol for the words

"<font color = "red">what we must take the sine of to get</font>"

is 

sin<sup>-1</sup>

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 <font color = "red">what we have to take the sine of to get</font> x"

which translates as

y = sin<sup>-1</sup>(x)

Edwin
AnlytcPhil@aol.com</pre>