# 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 one billion nine hundred thirty-five million one hundred twenty-three thousand five

### Interesting facts

• 1935123005 has 32 divisors, whose sum is 2531088000
• The reverse of 1935123005 is 5003215391
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 29
• Digital Root 2

### Name

Name one billion fifty-seven million two hundred fifty-nine thousand one hundred one

### Interesting facts

• 1057259101 has 4 divisors, whose sum is 1103226912
• The reverse of 1057259101 is 1019527501
• Previous prime number is 23

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 31
• Digital Root 4

### Name

Name one billion eight hundred ninety-two million thirty-six thousand nine hundred fifty

### Interesting facts

• 1892036950 has 16 divisors, whose sum is 3046792320
• The reverse of 1892036950 is 0596302981
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7