, ,

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

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Adjacent

Use the power rule to combine exponents.

Adjacent

Adjacent

Add and .

Adjacent

Adjacent

Raise to the power of .

Adjacent

Subtract from .

Adjacent

Rewrite as .

Factor out of .

Adjacent

Rewrite as .

Adjacent

Adjacent

Pull terms out from under the radical.

Adjacent

Adjacent

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)