# Trigonometry Examples

Step 1

Step 1.1

Subtract from both sides of the equation.

Step 1.2

Subtract from .

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 2.3

Simplify the right side.

Step 2.3.1

Move the negative in front of the fraction.

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 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.

Step 6

Step 6.1

Subtract from .

Step 6.2

The resulting angle of is positive, less than , and coterminal with .

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

Step 8.1

Add to to find the positive angle.

Step 8.2

To write as a fraction with a common denominator, multiply by .

Step 8.3

Combine fractions.

Step 8.3.1

Combine and .

Step 8.3.2

Combine the numerators over the common denominator.

Step 8.4

Simplify the numerator.

Step 8.4.1

Multiply by .

Step 8.4.2

Subtract from .

Step 8.5

List the new angles.

Step 9

The period of the function is so values will repeat every radians in both directions.

, for any integer