# Find the Other Trig Values in Quadrant III cos(x)=0

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 .
One to any power is one.
Opposite
Raising to any positive power yields .
Opposite
Multiply by .
Opposite
Opposite
Any root of is .
Opposite
Multiply by .
Opposite
Opposite
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Divide by .
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Division by results in tangent being undefined at .
Undefined
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Division by results in secant being undefined at .
Undefined
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Divide by .
This is the solution to each trig value.
Undefined
Find the Other Trig Values in Quadrant III cos(x)=0