Solve for ? 5sin(x)+1=3sin(x)

Solve for ? 5sin(x)+1=3sin(x)
Move all terms containing to the left side of the equation.
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Subtract from both sides of the equation.
Subtract from .
Subtract from both sides of the equation.
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 .
Move the negative in front of the fraction.
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 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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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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Multiply by .
Add and .
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 .
Add and .
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
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.
Tap for more steps...
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 eight hundred fourteen million nine hundred seventy-seven thousand thirty-four

Interesting facts

  • 814977034 has 16 divisors, whose sum is 1239533568
  • The reverse of 814977034 is 430779418
  • Previous prime number is 167

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7

Name

Name one billion eighty-one million three hundred sixty-five thousand six hundred sixty-nine

Interesting facts

  • 1081365669 has 8 divisors, whose sum is 1204117120
  • The reverse of 1081365669 is 9665631801
  • Previous prime number is 463

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name one billion three hundred nineteen million eight hundred twenty-six thousand eight hundred twenty-nine

Interesting facts

  • 1319826829 has 8 divisors, whose sum is 1346180472
  • The reverse of 1319826829 is 9286289131
  • Previous prime number is 961

Basic properties

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