Solve for ? sin(3x)=-1

Solve for ? sin(3x)=-1
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
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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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.
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.
Add and .
Multiply by .
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
Find the period.
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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 .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name seven hundred seventy-eight million eight hundred ninety-six thousand one hundred four

Interesting facts

  • 778896104 has 64 divisors, whose sum is 3134941056
  • The reverse of 778896104 is 401698877
  • Previous prime number is 7

Basic properties

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

Name

Name two hundred twenty-six million thirty-seven thousand eight hundred fifty-one

Interesting facts

  • 226037851 has 16 divisors, whose sum is 256838400
  • The reverse of 226037851 is 158730622
  • Previous prime number is 587

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7

Name

Name two hundred seventeen million seven hundred sixty-eight thousand five hundred seventy-eight

Interesting facts

  • 217768578 has 16 divisors, whose sum is 444804480
  • The reverse of 217768578 is 875867712
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6