Solve for x in Degrees 8sin(x)cos(x)+cos(x)=0

Solve for x in Degrees 8sin(x)cos(x)+cos(x)=0
Factor out of .
Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
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 .
Set equal to .
Solve for .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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.
Subtract from .
Find the period of .
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 degrees in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Move the negative in front of the fraction.
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
Evaluate .
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.
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
Find the period of .
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 .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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Name

Name one billion one hundred fifty-six million three hundred ninety-eight thousand nine hundred twenty-four

Interesting facts

• 1156398924 has 16 divisors, whose sum is 3469196808
• The reverse of 1156398924 is 4298936511
• Previous prime number is 3

Basic properties

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

Name

Name two hundred two million one hundred thirteen thousand forty-eight

Interesting facts

• 202113048 has 64 divisors, whose sum is 910440000
• The reverse of 202113048 is 840311202
• Previous prime number is 7499

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 21
• Digital Root 3

Name

Name two billion one hundred twenty-four million six hundred five thousand four hundred twenty-two

Interesting facts

• 2124605422 has 16 divisors, whose sum is 3380256000
• The reverse of 2124605422 is 2245064212
• Previous prime number is 131

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 28
• Digital Root 1