# Trigonometry Examples

,
Step 1
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.
Step 2
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.
Step 3
Replace the known values in the equation.
Step 4
Raise to the power of .
One to any power is one.
Multiply by .
Subtract from .
Step 5
Use the definition of tangent to find the value of .
Step 6
Substitute in the known values.
Step 7
Simplify the right side.
Multiply by .
Combine and simplify the denominator.
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: