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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
Multiply both sides of the equation by .
Step 3.3
Simplify the left side.
Step 3.3.1
Cancel the common factor of .
Step 3.3.1.1
Cancel the common factor.
Step 3.3.1.2
Rewrite the expression.
Step 3.4
To remove the radical on the left side of the equation, cube both sides of the equation.
Step 3.5
Simplify each side of the equation.
Step 3.5.1
Use to rewrite as .
Step 3.5.2
Simplify the left side.
Step 3.5.2.1
Simplify .
Step 3.5.2.1.1
Multiply the exponents in .
Step 3.5.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.5.2.1.1.2
Cancel the common factor of .
Step 3.5.2.1.1.2.1
Cancel the common factor.
Step 3.5.2.1.1.2.2
Rewrite the expression.
Step 3.5.2.1.2
Simplify.
Step 3.5.3
Simplify the right side.
Step 3.5.3.1
Simplify .
Step 3.5.3.1.1
Apply the product rule to .
Step 3.5.3.1.2
Raise to the power of .
Step 3.6
Add to both sides of the equation.
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
Apply the product rule to .
Step 5.2.3.2
Rewrite as .
Step 5.2.3.2.1
Use to rewrite as .
Step 5.2.3.2.2
Apply the power rule and multiply exponents, .
Step 5.2.3.2.3
Combine and .
Step 5.2.3.2.4
Cancel the common factor of .
Step 5.2.3.2.4.1
Cancel the common factor.
Step 5.2.3.2.4.2
Rewrite the expression.
Step 5.2.3.2.5
Simplify.
Step 5.2.3.3
Raise to the power of .
Step 5.2.3.4
Cancel the common factor of .
Step 5.2.3.4.1
Cancel the common factor.
Step 5.2.3.4.2
Rewrite the expression.
Step 5.2.4
Combine the opposite terms in .
Step 5.2.4.1
Add and .
Step 5.2.4.2
Add and .
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 the numerator.
Step 5.3.3.1
Subtract from .
Step 5.3.3.2
Add and .
Step 5.3.3.3
Rewrite as .
Step 5.3.3.4
Pull terms out from under the radical, assuming real numbers.
Step 5.3.4
Cancel the common factor of .
Step 5.3.4.1
Cancel the common factor.
Step 5.3.4.2
Divide by .
Step 5.4
Since and , then is the inverse of .