Solve for x f(x)*(2sin(x-pi/4))=0

Solve for x f(x)*(2sin(x-pi/4))=0
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Reorder factors in .
Simplify .
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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.
Divide by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Add to both sides of the equation.
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 the expression to find the second solution.
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Subtract from .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Simplify the right side of the equation.
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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 .
Add and .
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
Consolidate the answers.
, for any integer
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Name

Name one billion eight hundred eighty-two million six hundred forty-eight thousand five hundred five

Interesting facts

  • 1882648505 has 8 divisors, whose sum is 2267335752
  • The reverse of 1882648505 is 5058462881
  • Previous prime number is 277

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name five hundred seventy-one million five hundred twenty-eight thousand nine hundred thirty-three

Interesting facts

  • 571528933 has 4 divisors, whose sum is 605148300
  • The reverse of 571528933 is 339825175
  • Previous prime number is 17

Basic properties

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

Name

Name one billion three hundred ten million eight hundred ninety-eight thousand eight hundred ninety-one

Interesting facts

  • 1310898891 has 16 divisors, whose sum is 1806353408
  • The reverse of 1310898891 is 1988980131
  • Previous prime number is 31

Basic properties

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