,

Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Replace the known values in the equation.

Raise to the power of .

Adjacent

One to any power is one.

Adjacent

Multiply by .

Adjacent

Subtract from .

Adjacent

Adjacent

Use the definition of sine to find the value of .

Substitute in the known values.

Apply the sine double–angle identity.

Use the definition of to find the value of . In this case, .

Use the definition of to find the value of . In this case, .

Substitute the values into .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Trig Value sin(x)=1/4 , sin(2x)