Find the Other Trig Values in Quadrant I sin(theta)=0

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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One to any power is one.
Adjacent
Raising to any positive power yields .
Adjacent
Multiply by .
Adjacent
Add and .
Adjacent
Any root of is .
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.
Divide by .
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 .
Find the value of cotangent.
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Use the definition of cotangent to find the value of .
Substitute in the known values.
Division by results in cotangent being undefined at .
Undefined
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 .
Find the value of cosecant.
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Use the definition of cosecant to find the value of .
Substitute in the known values.
Division by results in cosecant being undefined at .
Undefined
This is the solution to each trig value.
Undefined
Find the Other Trig Values in Quadrant I sin(theta)=0

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