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

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
Apply the product rule to .
Adjacent
Multiply by by adding the exponents.
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Move .
Adjacent
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
Rewrite as .
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Rewrite as .
Adjacent
Apply the power rule and multiply exponents, .
Adjacent
Combine and .
Adjacent
Cancel the common factor of .
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Cancel the common factor.
Adjacent
Divide by .
Adjacent
Adjacent
Evaluate the exponent.
Adjacent
Adjacent
Simplify the expression.
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Multiply by .
Adjacent
Subtract from .
Adjacent
Adjacent
Adjacent
Find the value of cosine.
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Use the definition of cosine to find the value of .
Substitute in the known values.
Find the value of tangent.
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Use the definition of tangent to find the value of .
Substitute in the known values.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Find the value of cotangent.
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Use the definition of cotangent to find the value of .
Substitute in the known values.
Simplify the value of .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Multiply by .
Find the value of secant.
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Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
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Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Find the value of cosecant.
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Use the definition of cosecant to find the value of .
Substitute in the known values.
Simplify the value of .
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Multiply by .
Combine and simplify the denominator.
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Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
Tap for more steps…
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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