Trigonometry Examples

$d = 6 \cos (π t)$

Step 1

Rewrite the equation as $6 \cos (π t) = d$ .

$6 \cos (π t) = d$

Step 2

Divide each term in $6 \cos (π t) = d$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 \cos (π t) = d$ by $6$ .

$\frac{6 \cos (π t)}{6} = \frac{d}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 \cos (π t)}{6} = \frac{d}{6}$

Step 2.2.1.2

Divide $\cos (π t)$ by $1$ .

$\cos (π t) = \frac{d}{6}$

Step 3

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

$π t = \arccos (\frac{d}{6})$

Step 4

Divide each term in $π t = \arccos (\frac{d}{6})$ by $π$ and simplify.

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Step 4.1

Divide each term in $π t = \arccos (\frac{d}{6})$ by $π$ .

$\frac{π t}{π} = \frac{\arccos (\frac{d}{6})}{π}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $π$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{π t}{π} = \frac{\arccos (\frac{d}{6})}{π}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{\arccos (\frac{d}{6})}{π}$