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Trigonometry Examples
Step 1
Step 1.1
Set the denominator in equal to to find where the expression is undefined.
Step 1.2
Solve for .
Step 1.2.1
Simplify each term.
Step 1.2.1.1
Rewrite using the commutative property of multiplication.
Step 1.2.1.2
Multiply by by adding the exponents.
Step 1.2.1.2.1
Move .
Step 1.2.1.2.2
Multiply by .
Step 1.2.1.2.2.1
Raise to the power of .
Step 1.2.1.2.2.2
Use the power rule to combine exponents.
Step 1.2.1.2.3
Add and .
Step 1.2.1.3
Multiply by .
Step 1.2.2
Subtract from both sides of the equation.
Step 1.2.3
Add to both sides of the equation.
Step 1.2.4
Factor out of .
Step 1.2.4.1
Factor out of .
Step 1.2.4.2
Factor out of .
Step 1.2.4.3
Factor out of .
Step 1.2.5
Divide each term in by and simplify.
Step 1.2.5.1
Divide each term in by .
Step 1.2.5.2
Simplify the left side.
Step 1.2.5.2.1
Cancel the common factor of .
Step 1.2.5.2.1.1
Cancel the common factor.
Step 1.2.5.2.1.2
Divide by .
Step 1.2.5.3
Simplify the right side.
Step 1.2.5.3.1
Divide by .
Step 1.2.6
Add to both sides of the equation.
Step 1.2.7
Divide each term in by and simplify.
Step 1.2.7.1
Divide each term in by .
Step 1.2.7.2
Simplify the left side.
Step 1.2.7.2.1
Cancel the common factor of .
Step 1.2.7.2.1.1
Cancel the common factor.
Step 1.2.7.2.1.2
Divide by .
Step 1.2.8
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.9
Simplify .
Step 1.2.9.1
Rewrite as .
Step 1.2.9.2
Multiply by .
Step 1.2.9.3
Combine and simplify the denominator.
Step 1.2.9.3.1
Multiply by .
Step 1.2.9.3.2
Raise to the power of .
Step 1.2.9.3.3
Use the power rule to combine exponents.
Step 1.2.9.3.4
Add and .
Step 1.2.9.3.5
Rewrite as .
Step 1.2.9.3.5.1
Use to rewrite as .
Step 1.2.9.3.5.2
Apply the power rule and multiply exponents, .
Step 1.2.9.3.5.3
Combine and .
Step 1.2.9.3.5.4
Cancel the common factor of .
Step 1.2.9.3.5.4.1
Cancel the common factor.
Step 1.2.9.3.5.4.2
Rewrite the expression.
Step 1.2.9.3.5.5
Evaluate the exponent.
Step 1.2.9.4
Simplify the numerator.
Step 1.2.9.4.1
Rewrite as .
Step 1.2.9.4.2
Raise to the power of .
Step 1.2.9.5
Simplify the numerator.
Step 1.2.9.5.1
Combine using the product rule for radicals.
Step 1.2.9.5.2
Multiply by .
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Since the domain is not all real numbers, is not continuous over all real numbers.
Not continuous
Step 3