# Simplify cos(arcsin(5/13))

Simplify cos(arcsin(5/13))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Divide by .
One to any power is one.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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### Name

Name three hundred ninety million four hundred twenty-four thousand ninety-one

### Interesting facts

• 390424091 has 4 divisors, whose sum is 413390232
• The reverse of 390424091 is 190424093
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 32
• Digital Root 5

### Name

Name five hundred ninety-six million nine hundred eighty-two thousand two hundred sixteen

### Interesting facts

• 596982216 has 64 divisors, whose sum is 2696900832
• The reverse of 596982216 is 612289695
• Previous prime number is 257

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 48
• Digital Root 3

### Name

Name one billion eight hundred fifty-five million two hundred sixty-three thousand one hundred ninety-seven

### Interesting facts

• 1855263197 has 4 divisors, whose sum is 1919237820
• The reverse of 1855263197 is 7913625581
• Previous prime number is 29

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 47
• Digital Root 2