# Trigonometry Examples

Step 1

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .

Step 2

Use the sum formula for sine to simplify the expression. The formula states that .

Step 3

Remove parentheses.

Step 4

Step 4.1

The exact value of is .

Step 4.2

The exact value of is .

Step 4.3

Multiply .

Step 4.3.1

Multiply by .

Step 4.3.2

Multiply by .

Step 4.4

The exact value of is .

Step 4.5

The exact value of is .

Step 4.6

Multiply .

Step 4.6.1

Multiply by .

Step 4.6.2

Combine using the product rule for radicals.

Step 4.6.3

Multiply by .

Step 4.6.4

Multiply by .

Step 5

Combine the numerators over the common denominator.

Step 6

The result can be shown in multiple forms.

Exact Form:

Decimal Form: