Enter a problem...
Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Subtract from both sides of the equation.
Step 2.3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2.4
Simplify each side of the equation.
Step 2.4.1
Use to rewrite as .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Simplify .
Step 2.4.2.1.1
Multiply the exponents in .
Step 2.4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.4.2.1.1.2
Cancel the common factor of .
Step 2.4.2.1.1.2.1
Cancel the common factor.
Step 2.4.2.1.1.2.2
Rewrite the expression.
Step 2.4.2.1.2
Simplify.
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Simplify .
Step 2.4.3.1.1
Rewrite as .
Step 2.4.3.1.2
Expand using the FOIL Method.
Step 2.4.3.1.2.1
Apply the distributive property.
Step 2.4.3.1.2.2
Apply the distributive property.
Step 2.4.3.1.2.3
Apply the distributive property.
Step 2.4.3.1.3
Simplify and combine like terms.
Step 2.4.3.1.3.1
Simplify each term.
Step 2.4.3.1.3.1.1
Multiply by .
Step 2.4.3.1.3.1.2
Move to the left of .
Step 2.4.3.1.3.1.3
Multiply by .
Step 2.4.3.1.3.2
Subtract from .
Step 2.5
Solve for .
Step 2.5.1
Move all terms not containing to the right side of the equation.
Step 2.5.1.1
Add to both sides of the equation.
Step 2.5.1.2
Add and .
Step 2.5.2
Divide each term in by and simplify.
Step 2.5.2.1
Divide each term in by .
Step 2.5.2.2
Simplify the left side.
Step 2.5.2.2.1
Cancel the common factor of .
Step 2.5.2.2.1.1
Cancel the common factor.
Step 2.5.2.2.1.2
Divide by .
Step 2.5.2.3
Simplify the right side.
Step 2.5.2.3.1
Simplify each term.
Step 2.5.2.3.1.1
Cancel the common factor of and .
Step 2.5.2.3.1.1.1
Factor out of .
Step 2.5.2.3.1.1.2
Cancel the common factors.
Step 2.5.2.3.1.1.2.1
Factor out of .
Step 2.5.2.3.1.1.2.2
Cancel the common factor.
Step 2.5.2.3.1.1.2.3
Rewrite the expression.
Step 2.5.2.3.1.2
Move the negative in front of the fraction.
Step 2.5.2.3.1.3
Cancel the common factor of and .
Step 2.5.2.3.1.3.1
Factor out of .
Step 2.5.2.3.1.3.2
Cancel the common factors.
Step 2.5.2.3.1.3.2.1
Factor out of .
Step 2.5.2.3.1.3.2.2
Cancel the common factor.
Step 2.5.2.3.1.3.2.3
Rewrite the expression.
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
Simplify each term.
Step 4.2.3.1
Rewrite as .
Step 4.2.3.2
Expand using the FOIL Method.
Step 4.2.3.2.1
Apply the distributive property.
Step 4.2.3.2.2
Apply the distributive property.
Step 4.2.3.2.3
Apply the distributive property.
Step 4.2.3.3
Simplify and combine like terms.
Step 4.2.3.3.1
Simplify each term.
Step 4.2.3.3.1.1
Multiply by .
Step 4.2.3.3.1.2
Move to the left of .
Step 4.2.3.3.1.3
Multiply .
Step 4.2.3.3.1.3.1
Raise to the power of .
Step 4.2.3.3.1.3.2
Use the power rule to combine exponents.
Step 4.2.3.3.1.3.3
Add and .
Step 4.2.3.3.1.4
Rewrite as .
Step 4.2.3.3.1.4.1
Use to rewrite as .
Step 4.2.3.3.1.4.2
Apply the power rule and multiply exponents, .
Step 4.2.3.3.1.4.3
Combine and .
Step 4.2.3.3.1.4.4
Cancel the common factor of .
Step 4.2.3.3.1.4.4.1
Cancel the common factor.
Step 4.2.3.3.1.4.4.2
Rewrite the expression.
Step 4.2.3.3.1.4.5
Simplify.
Step 4.2.3.3.2
Subtract from .
Step 4.2.3.3.3
Add and .
Step 4.2.4
To write as a fraction with a common denominator, multiply by .
Step 4.2.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.2.5.1
Multiply by .
Step 4.2.5.2
Multiply by .
Step 4.2.6
Combine the numerators over the common denominator.
Step 4.2.7
Simplify each term.
Step 4.2.7.1
Simplify the numerator.
Step 4.2.7.1.1
Use to rewrite as .
Step 4.2.7.1.2
Use to rewrite as .
Step 4.2.7.1.3
Apply the distributive property.
Step 4.2.7.1.4
Multiply by .
Step 4.2.7.1.5
Apply the distributive property.
Step 4.2.7.1.6
Multiply by .
Step 4.2.7.1.7
Multiply by .
Step 4.2.7.1.8
Subtract from .
Step 4.2.7.1.9
Subtract from .
Step 4.2.7.1.10
Add and .
Step 4.2.7.1.11
Factor out of .
Step 4.2.7.1.11.1
Factor out of .
Step 4.2.7.1.11.2
Factor out of .
Step 4.2.7.1.11.3
Factor out of .
Step 4.2.7.2
Cancel the common factors.
Step 4.2.7.2.1
Factor out of .
Step 4.2.7.2.2
Cancel the common factor.
Step 4.2.7.2.3
Rewrite the expression.
Step 4.2.8
Simplify terms.
Step 4.2.8.1
Combine the numerators over the common denominator.
Step 4.2.8.2
Combine the opposite terms in .
Step 4.2.8.2.1
Add and .
Step 4.2.8.2.2
Add and .
Step 4.2.8.3
Cancel the common factor of .
Step 4.2.8.3.1
Cancel the common factor.
Step 4.2.8.3.2
Divide by .
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
Simplify each term.
Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Simplify.
Step 4.3.3.2.1
Cancel the common factor of .
Step 4.3.3.2.1.1
Cancel the common factor.
Step 4.3.3.2.1.2
Rewrite the expression.
Step 4.3.3.2.2
Cancel the common factor of .
Step 4.3.3.2.2.1
Move the leading negative in into the numerator.
Step 4.3.3.2.2.2
Factor out of .
Step 4.3.3.2.2.3
Cancel the common factor.
Step 4.3.3.2.2.4
Rewrite the expression.
Step 4.3.3.2.3
Multiply by .
Step 4.3.3.2.4
Cancel the common factor of .
Step 4.3.3.2.4.1
Factor out of .
Step 4.3.3.2.4.2
Cancel the common factor.
Step 4.3.3.2.4.3
Rewrite the expression.
Step 4.3.3.2.5
Multiply by .
Step 4.3.3.3
Subtract from .
Step 4.3.3.4
Factor using the perfect square rule.
Step 4.3.3.4.1
Rewrite as .
Step 4.3.3.4.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 4.3.3.4.3
Rewrite the polynomial.
Step 4.3.3.4.4
Factor using the perfect square trinomial rule , where and .
Step 4.3.3.5
Pull terms out from under the radical, assuming positive real numbers.
Step 4.3.4
Combine the opposite terms in .
Step 4.3.4.1
Subtract from .
Step 4.3.4.2
Add and .
Step 4.4
Since and , then is the inverse of .