Trigonometry Examples

Find the Inverse -2cos(3x-pi/4)
Step 1
Interchange the variables.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Rewrite the equation as .
Step 2.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Tap for more steps...
Step 2.2.2.1
Cancel the common factor of .
Tap for more steps...
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.
Tap for more steps...
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
Add to both sides of the equation.
Step 2.5
Divide each term in by and simplify.
Tap for more steps...
Step 2.5.1
Divide each term in by .
Step 2.5.2
Simplify the left side.
Tap for more steps...
Step 2.5.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.5.2.1.1
Cancel the common factor.
Step 2.5.2.1.2
Divide by .
Step 2.5.3
Simplify the right side.
Tap for more steps...
Step 2.5.3.1
Simplify each term.
Tap for more steps...
Step 2.5.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.5.3.1.2
Multiply .
Tap for more steps...
Step 2.5.3.1.2.1
Multiply by .
Step 2.5.3.1.2.2
Multiply by .
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
Tap for more steps...
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Tap for more steps...
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
Simplify each term.
Tap for more steps...
Step 4.2.3.1
Cancel the common factor of and .
Tap for more steps...
Step 4.2.3.1.1
Factor out of .
Step 4.2.3.1.2
Cancel the common factors.
Tap for more steps...
Step 4.2.3.1.2.1
Factor out of .
Step 4.2.3.1.2.2
Cancel the common factor.
Step 4.2.3.1.2.3
Rewrite the expression.
Step 4.2.3.1.2.4
Divide by .
Step 4.2.3.2
Multiply .
Tap for more steps...
Step 4.2.3.2.1
Multiply by .
Step 4.2.3.2.2
Multiply by .
Step 4.3
Evaluate .
Tap for more steps...
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
Simplify each term.
Tap for more steps...
Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Cancel the common factor of .
Tap for more steps...
Step 4.3.3.2.1
Cancel the common factor.
Step 4.3.3.2.2
Rewrite the expression.
Step 4.3.3.3
Cancel the common factor of .
Tap for more steps...
Step 4.3.3.3.1
Factor out of .
Step 4.3.3.3.2
Cancel the common factor.
Step 4.3.3.3.3
Rewrite the expression.
Step 4.3.4
Simplify by adding terms.
Tap for more steps...
Step 4.3.4.1
Combine the opposite terms in .
Tap for more steps...
Step 4.3.4.1.1
Combine the numerators over the common denominator.
Step 4.3.4.1.2
Subtract from .
Step 4.3.4.2
Simplify the expression.
Tap for more steps...
Step 4.3.4.2.1
Divide by .
Step 4.3.4.2.2
Add and .
Step 4.3.5
The functions cosine and arccosine are inverses.
Step 4.3.6
Cancel the common factor of .
Tap for more steps...
Step 4.3.6.1
Move the leading negative in into the numerator.
Step 4.3.6.2
Factor out of .
Step 4.3.6.3
Cancel the common factor.
Step 4.3.6.4
Rewrite the expression.
Step 4.3.7
Multiply.
Tap for more steps...
Step 4.3.7.1
Multiply by .
Step 4.3.7.2
Multiply by .
Step 4.4
Since and , then is the inverse of .