# Trigonometry Examples

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Use the definition of tangent 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

One to any power is one.

Hypotenuse

Remove parentheses around .

Hypotenuse

Raise to the power of .

Hypotenuse

Add and .

Hypotenuse

Hypotenuse

Use the definition of sine to find the value of .

Substitute in the known values.

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Multiply by .

The result can be shown in both exact and decimal forms.

Exact Form:

Decimal Form: