Trigonometry Examples

Find the Inverse cos(2)x-pi/3
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Evaluate .
Step 2.3
Add to both sides of the equation.
Step 2.4
Divide each term in by and simplify.
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Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Simplify each term.
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Step 2.4.3.1.1
Move the negative in front of the fraction.
Step 2.4.3.1.2
Multiply by .
Step 2.4.3.1.3
Factor out of .
Step 2.4.3.1.4
Separate fractions.
Step 2.4.3.1.5
Divide by .
Step 2.4.3.1.6
Divide by .
Step 2.4.3.1.7
Multiply by .
Step 2.4.3.1.8
Multiply the numerator by the reciprocal of the denominator.
Step 2.4.3.1.9
Divide by .
Step 2.4.3.1.10
Multiply .
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Step 2.4.3.1.10.1
Combine and .
Step 2.4.3.1.10.2
Multiply by .
Step 2.4.3.1.11
Divide by .
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
Simplify each term.
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Step 4.2.3.1
Evaluate .
Step 4.2.3.2
Apply the distributive property.
Step 4.2.3.3
Multiply .
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Step 4.2.3.3.1
Multiply by .
Step 4.2.3.3.2
Multiply by .
Step 4.2.3.4
Multiply .
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Step 4.2.3.4.1
Multiply by .
Step 4.2.3.4.2
Combine and .
Step 4.2.3.4.3
Multiply by .
Step 4.2.3.5
Divide by .
Step 4.2.4
Combine the opposite terms in .
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Step 4.2.4.1
Subtract from .
Step 4.2.4.2
Add and .
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 each term.
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Step 4.3.3.1
Evaluate .
Step 4.3.3.2
Apply the distributive property.
Step 4.3.3.3
Multiply .
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Step 4.3.3.3.1
Multiply by .
Step 4.3.3.3.2
Multiply by .
Step 4.3.3.4
Multiply by .
Step 4.3.4
Subtract from .
Step 4.4
Since and , then is the inverse of .