Trigonometry Examples

Find the Inverse f(x)=arctan(2x)
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Take the inverse arctangent of both sides of the equation to extract from inside the arctangent.
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
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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
The functions tangent and arctangent are inverses.
Step 5.2.4
Cancel the common factor of .
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Step 5.2.4.1
Cancel the common factor.
Step 5.2.4.2
Divide by .
Step 5.3
Evaluate .
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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
Cancel the common factor of .
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Step 5.3.3.1
Cancel the common factor.
Step 5.3.3.2
Rewrite the expression.
Step 5.4
Since and , then is the inverse of .