Trigonometry Examples

Find the Inverse cos(arccos(u))
Step 1
Interchange the variables.
Step 2
Solve for .
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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
Take the inverse arccosine of both sides of the equation to extract from inside the arccosine.
Step 2.4
Simplify the right side.
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Step 2.4.1
The functions cosine and arccosine are inverses.
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
Remove parentheses.
Step 4.2.4
The functions cosine and arccosine are inverses.
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
The functions cosine and arccosine are inverses.
Step 4.4
Since and , then is the inverse of .