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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 2.3
Subtract from both sides of the equation.
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Dividing two negative values results in a positive value.
Step 2.4.2.2
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Simplify each term.
Step 2.4.3.1.1
Move the negative one from the denominator of .
Step 2.4.3.1.2
Rewrite as .
Step 2.4.3.1.3
Dividing two negative values results in a positive value.
Step 2.4.3.1.4
Divide by .
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
Reorder and .
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 4.3.3
Simplify each term.
Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Multiply .
Step 4.3.3.2.1
Multiply by .
Step 4.3.3.2.2
Multiply by .
Step 4.3.4
Simplify by adding terms.
Step 4.3.4.1
Combine the opposite terms in .
Step 4.3.4.1.1
Combine the numerators over the common denominator.
Step 4.3.4.1.2
Subtract from .
Step 4.3.4.2
Simplify the expression.
Step 4.3.4.2.1
Divide by .
Step 4.3.4.2.2
Add and .
Step 4.3.5
The functions cosine and arccosine are inverses.
Step 4.4
Since and , then is the inverse of .