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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
Add to both sides of the equation.
Step 3.3
Divide each term in by and simplify.
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Cancel the common factor of .
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Step 3.3.3.1
Simplify each term.
Step 3.3.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 3.3.3.1.2
Multiply .
Step 3.3.3.1.2.1
Multiply by .
Step 3.3.3.1.2.2
Multiply by .
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
To write as a fraction with a common denominator, multiply by .
Step 5.2.3.1.2
Combine and .
Step 5.2.3.1.3
Combine the numerators over the common denominator.
Step 5.2.3.1.4
Multiply by .
Step 5.2.3.2
Multiply the numerator by the reciprocal of the denominator.
Step 5.2.3.3
Multiply .
Step 5.2.3.3.1
Multiply by .
Step 5.2.3.3.2
Multiply by .
Step 5.2.4
Simplify terms.
Step 5.2.4.1
Combine the numerators over the common denominator.
Step 5.2.4.2
Combine the opposite terms in .
Step 5.2.4.2.1
Add and .
Step 5.2.4.2.2
Add and .
Step 5.2.4.3
Cancel the common factor of .
Step 5.2.4.3.1
Cancel the common factor.
Step 5.2.4.3.2
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
Cancel the common factor.
Step 5.3.3.2.2
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 5.3.4
Combine the opposite terms in .
Step 5.3.4.1
Combine the numerators over the common denominator.
Step 5.3.4.2
Subtract from .
Step 5.3.4.3
Divide by .
Step 5.3.4.4
Add and .
Step 5.4
Since and , then is the inverse of .