# Trigonometry Examples

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.

Remove parentheses around .

Raise to the power of to get .

Remove parentheses around .

Rewrite as .

Multiply by to get .

Subtract from to get .

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.

Simplify the value of .

Combine and into a single radical.

Simplify by dividing numbers.

Divide by to get .

Any root of is .

Use the definition of secant 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 .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

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 .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Use the definition of cotangent to find the value of .

Substitute in the known values.

Simplify the value of .

Combine and into a single radical.

Simplify by dividing numbers.

Divide by to get .

Any root of is .

This is the solution to each trig value.