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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Divide each term in by and simplify.
Step 2.3.1
Divide each term in by .
Step 2.3.2
Simplify the left side.
Step 2.3.2.1
Cancel the common factor of .
Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Divide by .
Step 2.3.3
Simplify the right side.
Step 2.3.3.1
Move the negative in front of the fraction.
Step 2.4
Take the inverse arctangent of both sides of the equation to extract from inside the arctangent.
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
Combine the numerators over the common denominator.
Step 4.2.4
Combine the opposite terms in .
Step 4.2.4.1
Subtract from .
Step 4.2.4.2
Add and .
Step 4.2.5
Cancel the common factor of .
Step 4.2.5.1
Cancel the common factor.
Step 4.2.5.2
Divide by .
Step 4.2.6
The functions tangent and arctangent are inverses.
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 4.4
Since and , then is the inverse of .