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.

Raise to the power of .

Adjacent

Raise to the power of .

Adjacent

Multiply by .

Adjacent

Subtract from .

Adjacent

Rewrite as .

Adjacent

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

Adjacent

Adjacent

Use the definition of cosine to find the value of .

Substitute in the known values.

Use the definition of tangent to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of cotangent to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of secant to find the value of .

Substitute in the known values.

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 IV sin(t)=-5/13