# Find the Exact Value sec(arcsin(-1/2))

Find the Exact Value sec(arcsin(-1/2))
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 .
Simplify the denominator.
One to any power is one.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
One to any power is one.
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 denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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### Name

Name three hundred thirty-eight million three hundred thousand eight hundred fourteen

### Interesting facts

• 338300814 has 16 divisors, whose sum is 712212480
• The reverse of 338300814 is 418003833
• Previous prime number is 19

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 30
• Digital Root 3

### Name

Name four hundred thirty-seven million eight hundred eighty-three thousand four hundred five

### Interesting facts

• 437883405 has 8 divisors, whose sum is 467660416
• The reverse of 437883405 is 504388734
• Previous prime number is 817

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name four hundred twenty-five million five hundred sixty thousand five hundred thirty-nine

### Interesting facts

• 425560539 has 8 divisors, whose sum is 571222800
• The reverse of 425560539 is 935065524
• Previous prime number is 149

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 39
• Digital Root 3