Trigonometry Examples

$h = 15 \cos (\frac{π}{20} t)$

Step 1

Rewrite the equation as $15 \cos (\frac{π}{20} t) = h$ .

$15 \cos (\frac{π}{20} t) = h$

Step 2

Divide each term in $15 \cos (\frac{π}{20} t) = h$ by $15$ and simplify.

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Step 2.1

Divide each term in $15 \cos (\frac{π}{20} t) = h$ by $15$ .

$\frac{15 \cos (\frac{π}{20} t)}{15} = \frac{h}{15}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $15$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{15 \cos (\frac{π}{20} t)}{15} = \frac{h}{15}$

Step 2.2.1.2

Divide $\cos (\frac{π}{20} t)$ by $1$ .

$\cos (\frac{π}{20} t) = \frac{h}{15}$

Step 3

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

$\frac{π}{20} t = \arccos (\frac{h}{15})$

Step 4

Simplify the left side.

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Step 4.1

Combine $\frac{π}{20}$ and $t$ .

$\frac{π t}{20} = \arccos (\frac{h}{15})$

Step 5

Multiply both sides of the equation by $\frac{20}{π}$ .

$\frac{20}{π} \cdot \frac{π t}{20} = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{20}{π} \cdot \frac{π t}{20}$ .

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Step 6.1.1.1

Cancel the common factor of $20$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{20}{π} \cdot \frac{π t}{20} = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{π} (π t) = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6.1.1.2

Cancel the common factor of $π$ .

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Step 6.1.1.2.1

Factor $π$ out of $π t$ .

$\frac{1}{π} (π (t)) = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{π} (π t) = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6.1.1.2.3

Rewrite the expression.

$t = \frac{20}{π} \arccos (\frac{h}{15})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Combine $\frac{20}{π}$ and $\arccos (\frac{h}{15})$ .

$t = \frac{20 \arccos (\frac{h}{15})}{π}$