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

Factor out of .

Cancel the common factor.

Rewrite the expression.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Write as a fraction with a common denominator.

Combine the numerators over the common denominator.

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((7pi)/8)