Trigonometry Examples

Find the Exact Value tan((5pi)/12)
Split into two angles where the values of the six trigonometric functions are known.
Apply the sum of angles identity.
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
Simplify .
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify the denominator.
Multiply by .
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply and .
Expand the denominator using the FOIL method.
Simplify.
Simplify the numerator.
Reorder terms.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Combine using the product rule for radicals.
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
The result can be shown in multiple forms.
Exact Form:
Decimal Form: