Solve for x 2+2cos(x)=0

$2 + 2 \cos (x) = 0$

Subtract $2$ from both sides of the equation.

$2 \cos (x) = - 2$

Divide each term in $2 \cos (x) = - 2$ by $2$ and simplify.

Divide each term in $2 \cos (x) = - 2$ by $2$ .

$\frac{2 \cos (x)}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cos (x)}{2} = \frac{- 2}{2}$

Divide $\cos (x)$ by $1$ .

$\cos (x) = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$\cos (x) = - 1$

Take the inverse cosine of both sides of the equation to extract $x$ from inside the cosine.

$x = \arccos (- 1)$

Simplify the right side.

The exact value of $\arccos (- 1)$ is $π$ .

$x = π$

The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from $2 π$ to find the solution in the third quadrant.

$x = 2 π - π$

Subtract $π$ from $2 π$ .

$x = π$

Find the period of $\cos (x)$ .

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

The period of the $\cos (x)$ function is $2 π$ so values will repeat every $2 π$ radians in both directions.

$x = π + 2 π n$ , for any integer $n$

Solve for x 2+2cos(x)=0

Related Questions

Support LCMGCF.com by disabling your adblocker.