Solve for x sin(x)=( square root of 2)/2

Solve for x sin(x)=( square root of 2)/2
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Simplify .
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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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Move to the left of .
Subtract from .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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Name

Name one billion nine hundred six million five hundred eight thousand six hundred fifty-four

Interesting facts

  • 1906508654 has 16 divisors, whose sum is 2933990640
  • The reverse of 1906508654 is 4568056091
  • Previous prime number is 113

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name one billion forty-two million one hundred sixteen thousand seven hundred seven

Interesting facts

  • 1042116707 has 4 divisors, whose sum is 1042345800
  • The reverse of 1042116707 is 7076112401
  • Previous prime number is 4643

Basic properties

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

Name

Name one billion nine hundred fourteen million six hundred twenty-four thousand nine hundred fifty-eight

Interesting facts

  • 1914624958 has 4 divisors, whose sum is 2871937440
  • The reverse of 1914624958 is 8594264191
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4