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

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 .

In case any individual factor in the left part of the equation equals , the entire expression will be equal to .

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 .

Add.

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

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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