Enter a problem...
Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Move the negative in front of the fraction.
Step 2.3
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
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
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
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
Cancel the common factor of and .
Step 4.2.3.1
Factor out of .
Step 4.2.3.2
Cancel the common factors.
Step 4.2.3.2.1
Factor out of .
Step 4.2.3.2.2
Cancel the common factor.
Step 4.2.3.2.3
Rewrite the expression.
Step 4.2.3.2.4
Divide by .
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
Cancel the common factor of .
Step 4.3.3.1
Cancel the common factor.
Step 4.3.3.2
Rewrite the expression.
Step 4.3.4
The functions cosine and arccosine are inverses.
Step 4.3.5
Cancel the common factor of .
Step 4.3.5.1
Move the leading negative in into the numerator.
Step 4.3.5.2
Factor out of .
Step 4.3.5.3
Cancel the common factor.
Step 4.3.5.4
Rewrite the expression.
Step 4.3.6
Multiply.
Step 4.3.6.1
Multiply by .
Step 4.3.6.2
Multiply by .
Step 4.4
Since and , then is the inverse of .