Solve for x in Radians sin(3x)=-( square root of 3)/2

Solve for x in Radians sin(3x)=-( square root of 3)/2
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Multiply the numerator by the reciprocal of the denominator.
Multiply .
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Multiply by .
Multiply by .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Subtract from .
The resulting angle of is positive, less than , and coterminal with .
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Multiply the numerator by the reciprocal of the denominator.
Multiply .
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Multiply by .
Multiply by .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
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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Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
List the new angles.
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 hundred nine million four hundred forty-two thousand one hundred thirty

Interesting facts

  • 109442130 has 16 divisors, whose sum is 200123136
  • The reverse of 109442130 is 031244901
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 24
  • Digital Root 6

Name

Name five hundred seventy-eight million one hundred sixty-nine thousand six hundred eighty

Interesting facts

  • 578169680 has 256 divisors, whose sum is 3849120000
  • The reverse of 578169680 is 086961875
  • Previous prime number is 239

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 50
  • Digital Root 5

Name

Name one billion five hundred thirty-nine million five hundred fifty-one thousand nine hundred thirty-seven

Interesting facts

  • 1539551937 has 32 divisors, whose sum is 2563799040
  • The reverse of 1539551937 is 7391559351
  • Previous prime number is 593

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3