Trigonometry Examples

Find the Other Trig Values in Quadrant I
Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Simplify the right side.
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Remove parentheses around .
Opposite
Raise to the power of to get .
Opposite
Remove parentheses around .
Opposite
One to any power is one.
Opposite
Multiply by to get .
Opposite
Subtract from to get .
Opposite
Opposite
Find the value of sine.
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Use the definition of sine 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.
Divide by to get .
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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Multiply by .
Simplify.
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Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and to get .
Rewrite as .
Multiply by to get .
Find the value of secant.
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Use the definition of secant to find the value of .
Substitute in the known values.
Divide by to get .
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 .
Simplify.
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Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and to get .
Rewrite as .
This is the solution to each trig value.
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