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 .

To write as a fraction with a common denominator, multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Exact Value sin(arccos(1/2))