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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
To remove the radical on the left side of the equation, cube both sides of the equation.
Step 2.3
Simplify each side of the equation.
Step 2.3.1
Use to rewrite as .
Step 2.3.2
Simplify the left side.
Step 2.3.2.1
Simplify .
Step 2.3.2.1.1
Multiply the exponents in .
Step 2.3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.3.2.1.1.2
Cancel the common factor of .
Step 2.3.2.1.1.2.1
Cancel the common factor.
Step 2.3.2.1.1.2.2
Rewrite the expression.
Step 2.3.2.1.2
Simplify.
Step 2.4
Subtract from both sides of the equation.
Step 2.5
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 3
Replace with to show the final answer.
Step 4
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Rewrite as .
Step 4.2.3.1
Use to rewrite as .
Step 4.2.3.2
Apply the power rule and multiply exponents, .
Step 4.2.3.3
Combine and .
Step 4.2.3.4
Cancel the common factor of .
Step 4.2.3.4.1
Cancel the common factor.
Step 4.2.3.4.2
Rewrite the expression.
Step 4.2.3.5
Simplify.
Step 4.2.4
Combine the opposite terms in .
Step 4.2.4.1
Subtract from .
Step 4.2.4.2
Add and .
Step 4.3
Evaluate .
Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
The functions tangent and arctangent are inverses.
Step 4.3.4
Subtract from .
Step 4.3.5
Add and .
Step 4.3.6
Pull terms out from under the radical, assuming real numbers.
Step 4.4
Since and , then is the inverse of .