Trigonometry Examples

Find the Inverse tan(-(5x)/6)
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 2.3
Multiply both sides of the equation by .
Step 2.4
Simplify both sides of the equation.
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Step 2.4.1
Simplify the left side.
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Step 2.4.1.1
Simplify .
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Step 2.4.1.1.1
Cancel the common factor of .
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Step 2.4.1.1.1.1
Move the leading negative in into the numerator.
Step 2.4.1.1.1.2
Move the leading negative in into the numerator.
Step 2.4.1.1.1.3
Factor out of .
Step 2.4.1.1.1.4
Cancel the common factor.
Step 2.4.1.1.1.5
Rewrite the expression.
Step 2.4.1.1.2
Cancel the common factor of .
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Step 2.4.1.1.2.1
Factor out of .
Step 2.4.1.1.2.2
Cancel the common factor.
Step 2.4.1.1.2.3
Rewrite the expression.
Step 2.4.1.1.3
Multiply.
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Step 2.4.1.1.3.1
Multiply by .
Step 2.4.1.1.3.2
Multiply by .
Step 2.4.2
Simplify the right side.
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Step 2.4.2.1
Simplify .
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Step 2.4.2.1.1
Combine and .
Step 2.4.2.1.2
Move to the left of .
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
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Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
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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
Since is an odd function, rewrite as .
Step 4.3
Evaluate .
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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
Simplify the numerator.
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Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Combine and .
Step 4.3.4
Multiply by .
Step 4.3.5
Reduce the expression by cancelling the common factors.
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Step 4.3.5.1
Reduce the expression by cancelling the common factors.
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Step 4.3.5.1.1
Factor out of .
Step 4.3.5.1.2
Factor out of .
Step 4.3.5.1.3
Cancel the common factor.
Step 4.3.5.1.4
Rewrite the expression.
Step 4.3.5.2
Divide by .
Step 4.3.6
Cancel the common factor of and .
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Step 4.3.6.1
Factor out of .
Step 4.3.6.2
Cancel the common factors.
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Step 4.3.6.2.1
Factor out of .
Step 4.3.6.2.2
Cancel the common factor.
Step 4.3.6.2.3
Rewrite the expression.
Step 4.3.6.2.4
Divide by .
Step 4.3.7
The functions tangent and arctangent are inverses.
Step 4.4
Since and , then is the inverse of .