# Find the Exact Value sin((7pi)/8) Rewrite as an angle where the values of the six trigonometric functions are known divided by .
Apply the sine halfangle identity.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Change the to because sine is positive in the second quadrant.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
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)

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