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Trigonometry Examples
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Simplify each term.
Step 3.2.1
Combine and .
Step 3.2.2
Move to the left of .
Step 3.3
Subtract from both sides of the equation.
Step 3.4
Multiply both sides of the equation by .
Step 3.5
Simplify both sides of the equation.
Step 3.5.1
Simplify the left side.
Step 3.5.1.1
Simplify .
Step 3.5.1.1.1
Cancel the common factor of .
Step 3.5.1.1.1.1
Move the leading negative in into the numerator.
Step 3.5.1.1.1.2
Move the leading negative in into the numerator.
Step 3.5.1.1.1.3
Factor out of .
Step 3.5.1.1.1.4
Cancel the common factor.
Step 3.5.1.1.1.5
Rewrite the expression.
Step 3.5.1.1.2
Cancel the common factor of .
Step 3.5.1.1.2.1
Factor out of .
Step 3.5.1.1.2.2
Cancel the common factor.
Step 3.5.1.1.2.3
Rewrite the expression.
Step 3.5.1.1.3
Multiply.
Step 3.5.1.1.3.1
Multiply by .
Step 3.5.1.1.3.2
Multiply by .
Step 3.5.2
Simplify the right side.
Step 3.5.2.1
Simplify .
Step 3.5.2.1.1
Apply the distributive property.
Step 3.5.2.1.2
Combine and .
Step 3.5.2.1.3
Multiply .
Step 3.5.2.1.3.1
Multiply by .
Step 3.5.2.1.3.2
Multiply by .
Step 3.5.2.1.3.3
Multiply by .
Step 3.5.2.1.3.4
Multiply by .
Step 3.5.2.1.3.5
Multiply by .
Step 3.5.2.1.4
Move to the left of .
Step 4
Replace with to show the final answer.
Step 5
Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
Step 5.2.1
Set up the composite result function.
Step 5.2.2
Evaluate by substituting in the value of into .
Step 5.2.3
Simplify each term.
Step 5.2.3.1
Simplify the numerator.
Step 5.2.3.1.1
Combine and .
Step 5.2.3.1.2
Move to the left of .
Step 5.2.3.1.3
To write as a fraction with a common denominator, multiply by .
Step 5.2.3.1.4
To write as a fraction with a common denominator, multiply by .
Step 5.2.3.1.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 5.2.3.1.5.1
Multiply by .
Step 5.2.3.1.5.2
Multiply by .
Step 5.2.3.1.5.3
Multiply by .
Step 5.2.3.1.5.4
Multiply by .
Step 5.2.3.1.6
Combine the numerators over the common denominator.
Step 5.2.3.1.7
Simplify the numerator.
Step 5.2.3.1.7.1
Multiply by .
Step 5.2.3.1.7.2
Multiply by .
Step 5.2.3.2
Combine and .
Step 5.2.3.3
Reduce the expression by cancelling the common factors.
Step 5.2.3.3.1
Factor out of .
Step 5.2.3.3.2
Cancel the common factor.
Step 5.2.3.3.3
Rewrite the expression.
Step 5.2.3.4
Multiply the numerator by the reciprocal of the denominator.
Step 5.2.3.5
Multiply .
Step 5.2.3.5.1
Multiply by .
Step 5.2.3.5.2
Multiply by .
Step 5.2.4
Combine the numerators over the common denominator.
Step 5.2.5
Simplify each term.
Step 5.2.5.1
Apply the distributive property.
Step 5.2.5.2
Multiply by .
Step 5.2.5.3
Multiply by .
Step 5.2.6
Simplify terms.
Step 5.2.6.1
Combine the opposite terms in .
Step 5.2.6.1.1
Add and .
Step 5.2.6.1.2
Add and .
Step 5.2.6.2
Cancel the common factor of .
Step 5.2.6.2.1
Cancel the common factor.
Step 5.2.6.2.2
Divide by .
Step 5.3
Evaluate .
Step 5.3.1
Set up the composite result function.
Step 5.3.2
Evaluate by substituting in the value of into .
Step 5.3.3
Simplify each term.
Step 5.3.3.1
Apply the distributive property.
Step 5.3.3.2
Cancel the common factor of .
Step 5.3.3.2.1
Move the leading negative in into the numerator.
Step 5.3.3.2.2
Move the leading negative in into the numerator.
Step 5.3.3.2.3
Factor out of .
Step 5.3.3.2.4
Cancel the common factor.
Step 5.3.3.2.5
Rewrite the expression.
Step 5.3.3.3
Cancel the common factor of .
Step 5.3.3.3.1
Factor out of .
Step 5.3.3.3.2
Cancel the common factor.
Step 5.3.3.3.3
Rewrite the expression.
Step 5.3.3.4
Multiply by .
Step 5.3.3.5
Multiply by .
Step 5.3.3.6
Cancel the common factor of .
Step 5.3.3.6.1
Move the leading negative in into the numerator.
Step 5.3.3.6.2
Factor out of .
Step 5.3.3.6.3
Factor out of .
Step 5.3.3.6.4
Cancel the common factor.
Step 5.3.3.6.5
Rewrite the expression.
Step 5.3.3.7
Cancel the common factor of .
Step 5.3.3.7.1
Factor out of .
Step 5.3.3.7.2
Cancel the common factor.
Step 5.3.3.7.3
Rewrite the expression.
Step 5.3.3.8
Rewrite as .
Step 5.3.4
Combine the opposite terms in .
Step 5.3.4.1
Add and .
Step 5.3.4.2
Add and .
Step 5.4
Since and , then is the inverse of .