# Trigonometry Examples

Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Cancel the common factor of .
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 3
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 4
Simplify the right side.
Step 4.1
The exact value of is .
Step 5
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Step 6
Simplify .
Step 6.1
To write as a fraction with a common denominator, multiply by .
Step 6.2
Combine fractions.
Step 6.2.1
Combine and .
Step 6.2.2
Combine the numerators over the common denominator.
Step 6.3
Simplify the numerator.
Step 6.3.1
Move to the left of .
Step 6.3.2
Subtract from .
Step 7
Find the period of .
Step 7.1
The period of the function can be calculated using .
Step 7.2
Replace with in the formula for period.
Step 7.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 7.4
Divide by .
Step 8
The period of the function is so values will repeat every radians in both directions.
, for any integer