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

Math
, ,
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 .
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Raise to the power of .
Adjacent
Multiply by by adding the exponents.
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Multiply by .
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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 .
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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)


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