Algebra Examples

$x = \frac{1}{2} \cos (2 t + 1)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot \cos (2 t + 1) = x$ .

$\frac{1}{2} \cdot \cos (2 t + 1) = x$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cos (2 t + 1)) = 2 x$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \cos (2 t + 1))$ .

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Step 3.1.1

Combine $\frac{1}{2}$ and $\cos (2 t + 1)$ .

$2 \frac{\cos (2 t + 1)}{2} = 2 x$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

$2 \frac{\cos (2 t + 1)}{2} = 2 x$

Step 3.1.2.2

Rewrite the expression.

$\cos (2 t + 1) = 2 x$

Step 4

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

$2 t + 1 = \arccos (2 x)$

Step 5

Subtract $1$ from both sides of the equation.

$2 t = \arccos (2 x) - 1$

Step 6

Divide each term in $2 t = \arccos (2 x) - 1$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 t = \arccos (2 x) - 1$ by $2$ .

$\frac{2 t}{2} = \frac{\arccos (2 x)}{2} + \frac{- 1}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{\arccos (2 x)}{2} + \frac{- 1}{2}$

Step 6.2.1.2

Divide $t$ by $1$ .

$t = \frac{\arccos (2 x)}{2} + \frac{- 1}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$t = \frac{\arccos (2 x)}{2} - \frac{1}{2}$