Split into two angles where the values of the six trigonometric functions are known.

Apply the sum of angles identity.

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

Simplify each term.

Multiply .

Multiply and .

Multiply by .

Multiply .

Multiply and .

Combine using the product rule for radicals.

Multiply by .

Multiply by .

Combine the numerators over the common denominator.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Exact Value sin((5pi)/12)