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Trigonometry Examples
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 3.4
Multiply both sides of the equation by .
Step 3.5
Simplify the left side.
Step 3.5.1
Cancel the common factor of .
Step 3.5.1.1
Cancel the common factor.
Step 3.5.1.2
Rewrite the expression.
Step 4
Replace with to show the final answer.
Step 5
Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
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
Combine the opposite terms in .
Step 5.2.3.1
Subtract from .
Step 5.2.3.2
Add and .
Step 5.3
Evaluate .
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
Simplify each term.
Step 5.3.3.1
Cancel the common factor of .
Step 5.3.3.1.1
Cancel the common factor.
Step 5.3.3.1.2
Divide by .
Step 5.3.3.2
The functions cosine and arccosine are inverses.
Step 5.3.4
Combine the opposite terms in .
Step 5.3.4.1
Subtract from .
Step 5.3.4.2
Add and .
Step 5.4
Since and , then is the inverse of .