Rewrite as an angle where the values of the six trigonometric functions are known divided by .

Apply the sine half–angle identity.

Change the to because sine is positive in the first quadrant.

The exact value of is .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Multiply by .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

Rewrite as .

Simplify the denominator.

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(22.5 degrees )