First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .

Use the sum formula for sine to simplify the expression. The formula states that .

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

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:

Expand Using Sum/Difference Formulas sin((7pi)/12)