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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 sine of both sides of the equation to extract from inside the sine.
Step 2.3
Divide each term in by and simplify.
Step 2.3.1
Divide each term in by .
Step 2.3.2
Simplify the left side.
Step 2.3.2.1
Dividing two negative values results in a positive value.
Step 2.3.2.2
Divide by .
Step 2.3.3
Simplify the right side.
Step 2.3.3.1
Move the negative one from the denominator of .
Step 2.3.3.2
Rewrite as .
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
Since is an odd function, rewrite as .
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
Multiply .
Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Multiply by .
Step 4.3.4
The functions sine and arcsine are inverses.
Step 4.4
Since and , then is the inverse of .