# Trigonometry Examples

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Step 1
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.
Step 2
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.
Step 3
Replace the known values in the equation.
Step 4
Step 4.1
One to any power is one.
Hypotenuse
Step 4.2
Raise to the power of .
Hypotenuse
Step 4.3
Hypotenuse
Hypotenuse
Step 5
Use the definition of sine to find the value of .
Step 6
Substitute in the known values.
Step 7
Simplify the right side.
Step 7.1
Multiply by .
Step 7.2
Combine and simplify the denominator.
Step 7.2.1
Multiply by .
Step 7.2.2
Raise to the power of .
Step 7.2.3
Raise to the power of .
Step 7.2.4
Use the power rule to combine exponents.
Step 7.2.5
Step 7.2.6
Rewrite as .
Step 7.2.6.1
Use to rewrite as .
Step 7.2.6.2
Apply the power rule and multiply exponents, .
Step 7.2.6.3
Combine and .
Step 7.2.6.4
Cancel the common factor of .
Step 7.2.6.4.1
Cancel the common factor.
Step 7.2.6.4.2
Rewrite the expression.
Step 7.2.6.5
Evaluate the exponent.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: