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Trigonometry Examples
Step 1
Remove the absolute value term. This creates a on the right side of the equation because .
Step 2
Step 2.1
First, use the positive value of the to find the first solution.
Step 2.2
Move all terms not containing to the right side of the equation.
Step 2.2.1
Subtract from both sides of the equation.
Step 2.2.2
Subtract from .
Step 2.3
Multiply both sides of the equation by .
Step 2.4
Simplify both sides of the equation.
Step 2.4.1
Simplify the left side.
Step 2.4.1.1
Cancel the common factor of .
Step 2.4.1.1.1
Cancel the common factor.
Step 2.4.1.1.2
Rewrite the expression.
Step 2.4.2
Simplify the right side.
Step 2.4.2.1
Multiply by .
Step 2.5
Next, use the negative value of the to find the second solution.
Step 2.6
Move all terms not containing to the right side of the equation.
Step 2.6.1
Subtract from both sides of the equation.
Step 2.6.2
Subtract from .
Step 2.7
Multiply both sides of the equation by .
Step 2.8
Simplify both sides of the equation.
Step 2.8.1
Simplify the left side.
Step 2.8.1.1
Cancel the common factor of .
Step 2.8.1.1.1
Cancel the common factor.
Step 2.8.1.1.2
Rewrite the expression.
Step 2.8.2
Simplify the right side.
Step 2.8.2.1
Multiply by .
Step 2.9
The complete solution is the result of both the positive and negative portions of the solution.