Trigonometry Examples

$v = \cos (2 π t)$

Step 1

Rewrite the equation as $\cos (2 π t) = v$ .

$\cos (2 π t) = v$

Step 2

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

$2 π t = \arccos (v)$

Step 3

Divide each term in $2 π t = \arccos (v)$ by $2 π$ and simplify.

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Step 3.1

Divide each term in $2 π t = \arccos (v)$ by $2 π$ .

$\frac{2 π t}{2 π} = \frac{\arccos (v)}{2 π}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 π t}{2 π} = \frac{\arccos (v)}{2 π}$

Step 3.2.1.2

Rewrite the expression.

$\frac{π t}{π} = \frac{\arccos (v)}{2 π}$

Step 3.2.2

Cancel the common factor of $π$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{π t}{π} = \frac{\arccos (v)}{2 π}$

Step 3.2.2.2

Divide $t$ by $1$ .

$t = \frac{\arccos (v)}{2 π}$