Find the Exact Value tan(arcsin(1/2))

Find the Exact Value tan(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 .
Multiply the numerator by the reciprocal of the denominator.
Simplify the denominator.
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One to any power is one.
Apply the product rule to .
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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Rewrite as .
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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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 two billion one hundred fourteen million seventy-three thousand forty-five

Interesting facts

  • 2114073045 has 16 divisors, whose sum is 3221445120
  • The reverse of 2114073045 is 5403704112
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9

Name

Name one billion twenty-nine million nine hundred sixty-five thousand three hundred five

Interesting facts

  • 1029965305 has 16 divisors, whose sum is 1309770000
  • The reverse of 1029965305 is 5035699201
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion five hundred ten million five hundred seventy-one thousand eight hundred sixty-nine

Interesting facts

  • 1510571869 has 8 divisors, whose sum is 1543259520
  • The reverse of 1510571869 is 9681750151
  • Previous prime number is 6353

Basic properties

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