# Expand Using Sum/Difference Formulas cos((19pi)/12)

Expand Using Sum/Difference Formulas cos((19pi)/12)
First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .
Use the sum formula for cosine to simplify the expression. The formula states that .
The exact value of is .
Simplify .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
The exact value of is .
The exact value of is .
Simplify .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
The exact value of is .
Simplify each term.
Multiply .
Multiply and .
Multiply by .
Multiply .
Multiply by .
Multiply by .
Multiply and .
Combine using the product rule for radicals.
Multiply by .
Multiply by .
Simplify.
Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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### Name

Name four hundred ninety-four million nine hundred twelve thousand five hundred seven

### Interesting facts

• 494912507 has 4 divisors, whose sum is 496159536
• The reverse of 494912507 is 705219494
• Previous prime number is 397

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion four hundred sixteen million four hundred forty-seven thousand four hundred forty-six

### Interesting facts

• 1416447446 has 8 divisors, whose sum is 2249651880
• The reverse of 1416447446 is 6447446141
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 41
• Digital Root 5

### Name

Name two hundred forty-four million nine hundred ninety-four thousand one hundred two

### Interesting facts

• 244994102 has 8 divisors, whose sum is 367756200
• The reverse of 244994102 is 201499442
• Previous prime number is 1409

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8