Trigonometry Examples

Find the Inverse cos(150/400)^a
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 natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.3
Expand the left side.
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Step 2.3.1
Expand by moving outside the logarithm.
Step 2.3.2
Reduce the expression by cancelling the common factors.
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Step 2.3.2.1
Factor out of .
Step 2.3.2.2
Factor out of .
Step 2.3.2.3
Cancel the common factor.
Step 2.3.2.4
Rewrite the expression.
Step 2.4
Simplify the left side.
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Step 2.4.1
Evaluate .
Step 2.5
Divide each term in by and simplify.
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Step 2.5.1
Divide each term in by .
Step 2.5.2
Simplify the left side.
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Step 2.5.2.1
Cancel the common factor of .
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Step 2.5.2.1.1
Cancel the common factor.
Step 2.5.2.1.2
Divide by .
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
Expand by moving outside the logarithm.
Step 4.2.4
Cancel the common factor of and .
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Step 4.2.4.1
Factor out of .
Step 4.2.4.2
Cancel the common factors.
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Step 4.2.4.2.1
Factor out of .
Step 4.2.4.2.2
Cancel the common factor.
Step 4.2.4.2.3
Rewrite the expression.
Step 4.2.5
Evaluate .
Step 4.2.6
Cancel the common factor of .
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Step 4.2.6.1
Cancel the common factor.
Step 4.2.6.2
Divide 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 and .
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Step 4.3.3.1
Factor out of .
Step 4.3.3.2
Cancel the common factors.
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Step 4.3.3.2.1
Factor out of .
Step 4.3.3.2.2
Cancel the common factor.
Step 4.3.3.2.3
Rewrite the expression.
Step 4.3.4
Evaluate .
Step 4.3.5
Use the change of base rule .
Step 4.3.6
Exponentiation and log are inverse functions.
Step 4.4
Since and , then is the inverse of .