Solving Arcsine Functions
How to solve arcsine function problems: definition, examples, and their solutions.
y = arcsin x is the inverse function of y = sin x.
Of course the graph of y = sin x
is not one-to-one:
it fails the horizontal line test.
So, to define the inverse function,
the domain of y = sin x is fixed like this:
-π/2 ≤ x ≤ π/2.
Graphing sine functions
Sine and arcsine functions
are each other's inverse function.
So sin (arcsin 0.4) = 0.4.
Set x = arcsin 1/2.
Next, sine both sides.
(left side) = sin x
(right side) = sin (arcsin 1/2)
So sin x = 1/2.
(-π/2 ≤ x ≤ π/2)
So x = 30º (⋅π/180)