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

Solve for x in Radians 2sin(pi/3x) = square root of 2
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 .
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the left side.
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Combine and .
Simplify the right side.
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The exact value of is .
Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
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Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine and .
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.
Solve for .
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Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
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Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Subtract from .
Simplify terms.
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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply 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 four hundred fifty-nine million six hundred sixty-one thousand seven hundred thirty-four

Interesting facts

  • 459661734 has 16 divisors, whose sum is 701256960
  • The reverse of 459661734 is 437166954
  • Previous prime number is 1181

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 45
  • Digital Root 9

Name

Name one billion five hundred twenty-four million five hundred thirty-two thousand nine hundred thirty-four

Interesting facts

  • 1524532934 has 4 divisors, whose sum is 2286799404
  • The reverse of 1524532934 is 4392354251
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2

Name

Name one billion twenty-five million five hundred forty-four thousand five hundred four

Interesting facts

  • 1025544504 has 128 divisors, whose sum is 4710182400
  • The reverse of 1025544504 is 4054455201
  • Previous prime number is 131

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 30
  • Digital Root 3