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Trigonometry Examples
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
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.
Step 2.2.3.1
Divide by .
Step 3
Set the denominator in equal to to find where the expression is undefined.
Step 4
Step 4.1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 4.2
Simplify each side of the equation.
Step 4.2.1
Use to rewrite as .
Step 4.2.2
Simplify the left side.
Step 4.2.2.1
Simplify .
Step 4.2.2.1.1
Multiply the exponents in .
Step 4.2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 4.2.2.1.1.2
Cancel the common factor of .
Step 4.2.2.1.1.2.1
Cancel the common factor.
Step 4.2.2.1.1.2.2
Rewrite the expression.
Step 4.2.2.1.2
Simplify.
Step 4.2.3
Simplify the right side.
Step 4.2.3.1
Raising to any positive power yields .
Step 4.3
Solve for .
Step 4.3.1
Subtract from both sides of the equation.
Step 4.3.2
Divide each term in by and simplify.
Step 4.3.2.1
Divide each term in by .
Step 4.3.2.2
Simplify the left side.
Step 4.3.2.2.1
Cancel the common factor of .
Step 4.3.2.2.1.1
Cancel the common factor.
Step 4.3.2.2.1.2
Divide by .
Step 4.3.2.3
Simplify the right side.
Step 4.3.2.3.1
Divide by .
Step 5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 6