# Trigonometry Examples

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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.

Adjacent

Raise to the power of .

Adjacent

Remove parentheses.

Adjacent

One to any power is one.

Adjacent

Multiply by .

Adjacent

Subtract from .

Adjacent

Adjacent

Use the definition of secant 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 .

The result can be shown in multiple forms.

Exact Form:

Decimal Form: