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.

Raise to the power of .

Opposite

Raise to the power of .

Opposite

Multiply by .

Opposite

Subtract from .

Opposite

Rewrite as .

Opposite

Multiply.

Pull terms out from under the radical, assuming positive real numbers.

Opposite

Multiply by .

Opposite

Opposite

Opposite

Use the definition of sine to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of tangent to find the value of .

Substitute in the known values.

Dividing two negative values results in a positive value.

Use the definition of cotangent to find the value of .

Substitute in the known values.

Dividing two negative values results in a positive value.

Use the definition of secant to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of cosecant to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

This is the solution to each trig value.

Find the Other Trig Values in Quadrant III cos(theta)=-12/37