Solve for t in Radians 2sin(t)^2-cos(t)-1=0

Solve for t in Radians 2sin(t)^2-cos(t)-1=0
Replace the with based on the identity.
Simplify each term.
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Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Substitute for .
Factor the left side of the equation.
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Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor.
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Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Solve for .
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Add to both sides of the equation.
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 .
Set equal to and solve for .
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Set equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Substitute for .
Set up each of the solutions to solve for .
Solve for in .
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Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
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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Multiply by .
Subtract from .
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 .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Solve for in .
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Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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The exact value of is .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Subtract from .
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 .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the solutions.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name one billion five hundred thirty-nine million eight hundred ninety-three thousand thirty-nine

Interesting facts

  • 1539893039 has 8 divisors, whose sum is 1596396672
  • The reverse of 1539893039 is 9303989351
  • Previous prime number is 233

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5

Name

Name eight hundred eighty-seven million five hundred seventeen thousand eight hundred eighty-seven

Interesting facts

  • 887517887 has 4 divisors, whose sum is 890817480
  • The reverse of 887517887 is 788715788
  • Previous prime number is 269

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 59
  • Digital Root 5

Name

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

Interesting facts

  • 1988524530 has 8 divisors, whose sum is 3049071084
  • The reverse of 1988524530 is 0354258891
  • Previous prime number is 45

Basic properties

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