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Trigonometry Examples
Step 1
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.
Step 2
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.
Step 3
Replace the known values in the equation.
Step 4
Step 4.1
Raise to the power of .
Opposite
Step 4.2
Raise to the power of .
Opposite
Step 4.3
Multiply by .
Opposite
Step 4.4
Subtract from .
Opposite
Step 4.5
Rewrite as .
Opposite
Step 4.6
Pull terms out from under the radical, assuming positive real numbers.
Opposite
Opposite
Step 5
Step 5.1
Use the definition of sine to find the value of .
Step 5.2
Substitute in the known values.
Step 6
Move the negative in front of the fraction.
Step 7
Step 7.1
Use the definition of tangent to find the value of .
Step 7.2
Substitute in the known values.
Step 7.3
Move the negative in front of the fraction.
Step 8
Step 8.1
Use the definition of cotangent to find the value of .
Step 8.2
Substitute in the known values.
Step 8.3
Move the negative in front of the fraction.
Step 9
Step 9.1
Use the definition of secant to find the value of .
Step 9.2
Substitute in the known values.
Step 9.3
Move the negative in front of the fraction.
Step 10
Step 10.1
Use the definition of cosecant to find the value of .
Step 10.2
Substitute in the known values.
Step 11
This is the solution to each trig value.