Use the definition of cotangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

Replace the known values in the equation.

One to any power is one.

Hypotenuse

Raising to any positive power yields .

Hypotenuse

Add and .

Hypotenuse

Any root of is .

Hypotenuse

Hypotenuse

Use the definition of sine to find the value of .

Substitute in the known values.

Divide by .

Use the definition of cosine to find the value of .

Substitute in the known values.

Divide by .

Use the definition of tangent to find the value of .

Substitute in the known values.

Division by results in tangent being undefined at .

Undefined

Use the definition of secant to find the value of .

Substitute in the known values.

Division by results in secant being undefined at .

Undefined

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 I cot(theta)=0