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

,
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.
Simplify .
Raise to the power of .
One to any power is one.
Multiply by .
Subtract from .
Use the definition of sine to find the value of .
Substitute in the known values.
Apply the sine doubleangle 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 .
Evaluate to find .
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)