# Trigonometry Examples

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.

Remove parentheses around .

Opposite

Raise to the power of to get .

Opposite

Remove parentheses around .

Opposite

One to any power is one.

Opposite

Multiply by to get .

Opposite

Subtract from to get .

Opposite

Opposite

Use the definition of sine 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.

Divide by to get .

Use the definition of cotangent 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 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.

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 .

This is the solution to each trig value.