# Find the Trig Value sin(x)=-( square root of 2)/2

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 .
Apply the product rule to .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Simplify the expression.
Multiply by .
Subtract from .
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Simplify the value of .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Multiply by .
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Simplify the value of .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Rewrite as .
This is the solution to each trig value.
Find the Trig Value sin(x)=-( square root of 2)/2
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