# Trigonometry Examples

Move all terms containing to the left side of the equation.
Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.
Subtract from to get .
Divide each term by and simplify.
Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Simplify the expression.
Multiply by to get .
Rewrite as .
Move the negative in front of the fraction.
Simplify the expression to find the first solution.
Take the inverse of both sides of the equation to extract from inside the .
The exact value of is .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Multiply by to get .
Move to the left of the expression .
Multiply by to get .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of the expression .
Multiply by to get .
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by to get .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Multiply by to get .
Subtract from to get .
Simplify the expression.
Move to the left of the expression .
Multiply by to get .
List the new angles.
The period of the function is so values will repeat every radians in both directions.

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