Enter a problem...
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
Divide each term in by and simplify.
Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of .
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.3
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
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
Cancel the common factor of .
Step 5.2.3.1
Cancel the common factor.
Step 5.2.3.2
Divide by .
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
The functions cosine and arccosine are inverses.
Step 5.3.4
Cancel the common factor of .
Step 5.3.4.1
Cancel the common factor.
Step 5.3.4.2
Rewrite the expression.
Step 5.4
Since and , then is the inverse of .