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Trigonometry Examples
Step 1
Step 1.1
Move all terms not containing to the right side of the equation.
Step 1.1.1
Subtract from both sides of the equation.
Step 1.1.2
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Cancel the common factor of .
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Cancel the common factor of and .
Step 1.2.3.1.1.1
Factor out of .
Step 1.2.3.1.1.2
Cancel the common factors.
Step 1.2.3.1.1.2.1
Factor out of .
Step 1.2.3.1.1.2.2
Cancel the common factor.
Step 1.2.3.1.1.2.3
Rewrite the expression.
Step 1.2.3.1.1.2.4
Divide by .
Step 1.2.3.1.2
Divide by .
Step 2
Step 2.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2.2
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Remove parentheses.
Step 3.2.2
Simplify each term.
Step 3.2.2.1
Rewrite as .
Step 3.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.2.3
Multiply by .
Step 3.2.3
Subtract from .
Step 3.2.4
The final answer is .
Step 4
The radical expression end point is .
Step 5
Step 5.1
Substitute the value into . In this case, the point is .
Step 5.1.1
Replace the variable with in the expression.
Step 5.1.2
Simplify the result.
Step 5.1.2.1
Remove parentheses.
Step 5.1.2.2
Simplify each term.
Step 5.1.2.2.1
Any root of is .
Step 5.1.2.2.2
Multiply by .
Step 5.1.2.3
Subtract from .
Step 5.1.2.4
The final answer is .
Step 5.2
Substitute the value into . In this case, the point is .
Step 5.2.1
Replace the variable with in the expression.
Step 5.2.2
Simplify the result.
Step 5.2.2.1
Remove parentheses.
Step 5.2.2.2
The final answer is .
Step 5.3
The square root can be graphed using the points around the vertex
Step 6