Solving Arccosine Functions
How to solve arccosine function problems: definition, example, and its solution.
y = arccos x is the inverse function of y = cos x.
Of course the graph of y = cos x
is not one-to-one:
it fails the horizontal line test.
So, to define the inverse function,
the domain of y = cos x is fixed like this:
0 ≤ x ≤ π.
Graphing cosine functions
Set x = arccos (-√2/2).
Next, cosine both sides.
(left side) = cos x
(right side) = cos (arccos [-√2/2])
So cos x = -√2/2.
(0 ≤ x ≤ π)
To solve cos x = -√2/2,
draw a right triangle that satisfies
cos x = -√2 / 2
= -1 / √2.
So cos x = (adjacent side) / (hypotenuse) = -1 / √2.
The right triangle is a 45-45-90 triangle.
So (opposite side) = 1.
The reference angle is π/4. (brown)
So x = π - π/4