Trigonometry Examples

Find the Other Trig Values in Quadrant I sin(theta)=12/13
Step 1
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.
Step 2
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.
Step 3
Replace the known values in the equation.
Step 4
Simplify inside the radical.
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Step 4.1
Raise to the power of .
Adjacent
Step 4.2
Raise to the power of .
Adjacent
Step 4.3
Multiply by .
Adjacent
Step 4.4
Subtract from .
Adjacent
Step 4.5
Rewrite as .
Adjacent
Step 4.6
Pull terms out from under the radical, assuming positive real numbers.
Adjacent
Adjacent
Step 5
Find the value of cosine.
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Step 5.1
Use the definition of cosine to find the value of .
Step 5.2
Substitute in the known values.
Step 6
Find the value of tangent.
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Step 6.1
Use the definition of tangent to find the value of .
Step 6.2
Substitute in the known values.
Step 7
Find the value of cotangent.
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Step 7.1
Use the definition of cotangent to find the value of .
Step 7.2
Substitute in the known values.
Step 8
Find the value of secant.
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Step 8.1
Use the definition of secant to find the value of .
Step 8.2
Substitute in the known values.
Step 9
Find the value of cosecant.
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Step 9.1
Use the definition of cosecant to find the value of .
Step 9.2
Substitute in the known values.
Step 10
This is the solution to each trig value.