# Evaluate cos(arcsin(1/2))

Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Divide by .
One to any power is one.
Apply the product rule to .
One to any power is one.
Raise to the power of .
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Subtract from .
Rewrite as .
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical.
The absolute value is the distance between a number and zero. The distance between and is .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate cos(arcsin(1/2))