# Trigonometry Examples

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.

Remove parentheses around .

Hypotenuse

Raise to the power of to get .

Hypotenuse

Remove parentheses around .

Hypotenuse

One to any power is one.

Hypotenuse

Add and to get .

Hypotenuse

Hypotenuse

Use the definition of sine to find the value of .

Substitute in the known values.

Simplify the value of .

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and to get .

Rewrite as .

Use the definition of cosine to find the value of .

Substitute in the known values.

Simplify the value of .

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and to get .

Rewrite as .

Multiply by to get .

Use the definition of tangent to find the value of .

Substitute in the known values.

Divide by to get .

Use the definition of secant to find the value of .

Substitute in the known values.

Divide by to get .

Use the definition of cosecant to find the value of .

Substitute in the known values.

This is the solution to each trig value.