# Trigonometry Examples

Step 1

Add to both sides of the equation.

Step 2

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

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

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

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