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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
Add to both sides of the equation.
Step 1.1.2
Combine the opposite terms in .
Step 1.1.2.1
Add and .
Step 1.1.2.2
Add and .
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
Cancel the common factor of and .
Step 1.2.3.1.1
Factor out of .
Step 1.2.3.1.2
Cancel the common factors.
Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factor.
Step 1.2.3.1.2.3
Rewrite the expression.
Step 1.2.3.1.2.4
Divide by .
Step 2
Step 2.1
To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .
Step 2.2
Add to both sides of the equation.
Step 2.3
Replace the variable with in the expression.
Step 2.4
Simplify .
Step 2.4.1
Subtract from .
Step 2.4.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.4.3
Multiply by .
Step 2.5
The absolute value vertex is .
Step 3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Step 4
Step 4.1
Substitute the value into . In this case, the point is .
Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
Step 4.1.2.1
Subtract from .
Step 4.1.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.1.2.3
Multiply by .
Step 4.1.2.4
The final answer is .
Step 4.2
Substitute the value into . In this case, the point is .
Step 4.2.1
Replace the variable with in the expression.
Step 4.2.2
Simplify the result.
Step 4.2.2.1
Subtract from .
Step 4.2.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.2.2.3
Multiply by .
Step 4.2.2.4
The final answer is .
Step 4.3
Substitute the value into . In this case, the point is .
Step 4.3.1
Replace the variable with in the expression.
Step 4.3.2
Simplify the result.
Step 4.3.2.1
Subtract from .
Step 4.3.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.3.2.3
Multiply by .
Step 4.3.2.4
The final answer is .
Step 4.4
The absolute value can be graphed using the points around the vertex
Step 5