# Solve for ? two cos(x) to the power of two plus square root of three cos(x) equals zero

Solve for ? 2cos(x)^2+ square root of 3cos(x)=0
The left part of the equation should be factored.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Replace the left side with the factored expression.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
In case any individual factor in the left part of the equation equals , the entire expression will be equal to .
Make the initial factor equal to and solve.
Set the Initially factor equal to .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
The 1st and 4th quadrants of the cosine function are positive. To calculate the second answer, subtract the reference angle from to find the solution in the fourth quadrant.
Clarify .
To write as a fraction with a common denominator, First, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
First, multiply by .
Add numerators over the common denominator.
Clarify the numerator.
Multiply by .
Subtract from .
Calculate the period.
Evaluate the period of function using .
Replace with in the formula for period.
Find solution to the equation.
The absolute value is the distance between a number and zero. The distance between and is .
First, divide by .
The period of the function is so values will repeat every radians in two directions at once.
, for any integer
, for any integer
Make the following factor equal to and solve.
Set the Then factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
The common factor should be canceled of .
Cancel the common factor.
Divide by .
Put the negative in front of the fraction.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
The cosine function is negative in the second and third quadrants. To calculate the second answer, subtract the reference angle from to find the solution in the third quadrant.
Simplify .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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