Trigonometry Examples

Find the Inverse y=-1/6sin(x/4)
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Multiply both sides of the equation by .
Step 2.3
Simplify the left side.
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Step 2.3.1
Simplify .
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Step 2.3.1.1
Combine and .
Step 2.3.1.2
Cancel the common factor of .
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Step 2.3.1.2.1
Move the leading negative in into the numerator.
Step 2.3.1.2.2
Factor out of .
Step 2.3.1.2.3
Cancel the common factor.
Step 2.3.1.2.4
Rewrite the expression.
Step 2.3.1.3
Multiply.
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Step 2.3.1.3.1
Multiply by .
Step 2.3.1.3.2
Multiply by .
Step 2.4
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 2.5
Multiply both sides of the equation by .
Step 2.6
Simplify the left side.
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Step 2.6.1
Cancel the common factor of .
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Step 2.6.1.1
Cancel the common factor.
Step 2.6.1.2
Rewrite the expression.
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
Combine and .
Step 4.2.4
Cancel the common factor of .
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Step 4.2.4.1
Move the leading negative in into the numerator.
Step 4.2.4.2
Factor out of .
Step 4.2.4.3
Cancel the common factor.
Step 4.2.4.4
Rewrite the expression.
Step 4.2.5
Multiply.
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Step 4.2.5.1
Multiply by .
Step 4.2.5.2
Multiply by .
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
Cancel the common factor of .
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Step 4.3.3.1
Cancel the common factor.
Step 4.3.3.2
Divide by .
Step 4.3.4
The functions sine and arcsine are inverses.
Step 4.3.5
Cancel the common factor of .
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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.
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Step 4.3.6.1
Multiply by .
Step 4.3.6.2
Multiply by .
Step 4.4
Since and , then is the inverse of .