# Solve for θ in Radians sin(2theta)+ square root of 3cos(theta)=0

Solve for θ in Radians sin(2theta)+ square root of 3cos(theta)=0
Apply the sine double-angle identity.
Factor out of .
Factor out 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.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
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 radians 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.
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.
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.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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
, 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 seven hundred twenty million four hundred seventy-nine thousand five hundred twenty-two

### Interesting facts

• 720479522 has 16 divisors, whose sum is 1235656512
• The reverse of 720479522 is 225974027
• Previous prime number is 20333

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name one billion six million eight hundred four thousand three hundred eighty-four

### Interesting facts

• 1006804384 has 128 divisors, whose sum is 7657182720
• The reverse of 1006804384 is 4834086001
• Previous prime number is 659

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 34
• Digital Root 7

### Name

Name three million nine hundred fifty-five thousand four hundred seventy-six

### Interesting facts

• 3955476 has 32 divisors, whose sum is 9492480
• The reverse of 3955476 is 6745593
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 7
• Sum of Digits 39
• Digital Root 3