Algebra Examples

$\cos^{2} (x) = - 1$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$\cos (x) = \pm \sqrt{- 1}$

Step 2

Rewrite $\sqrt{- 1}$ as $i$ .

$\cos (x) = \pm i$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$\cos (x) = i$

Step 3.2

Next, use the negative value of the $\pm$ to find the second solution.

$\cos (x) = - i$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

$\cos (x) = i, - i$

Step 4

Set up each of the solutions to solve for $x$ .

$\cos (x) = i$

$\cos (x) = - i$

Step 5

Solve for $x$ in $\cos (x) = i$ .

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Step 5.1

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

$x = \arccos (i)$

Step 5.2

The inverse cosine of $\arccos (i)$ is undefined.

Undefined

Step 6

Solve for $x$ in $\cos (x) = - i$ .

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Step 6.1

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

$x = \arccos (- i)$

Step 6.2

The inverse cosine of $\arccos (- i)$ is undefined.

Undefined

Step 7

List all of the solutions.

No solution