# Find the Trig Value sin(x)=-1/5 , pi<x<(3pi)/2 , cos(x)

, ,
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 .
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Subtract from .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Use the definition of cosine to find the value of .
Substitute in the known values.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Find the Trig Value sin(x)=-1/5 , pi<x<(3pi)/2 , cos(x)