Trigonometry Examples

$h = 7 \cos (\frac{π}{3} t)$

Step 1

Rewrite the equation as $7 \cos (\frac{π}{3} t) = h$ .

$7 \cos (\frac{π}{3} t) = h$

Step 2

Divide each term in $7 \cos (\frac{π}{3} t) = h$ by $7$ and simplify.

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Step 2.1

Divide each term in $7 \cos (\frac{π}{3} t) = h$ by $7$ .

$\frac{7 \cos (\frac{π}{3} t)}{7} = \frac{h}{7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 \cos (\frac{π}{3} t)}{7} = \frac{h}{7}$

Step 2.2.1.2

Divide $\cos (\frac{π}{3} t)$ by $1$ .

$\cos (\frac{π}{3} t) = \frac{h}{7}$

Step 3

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

$\frac{π}{3} t = \arccos (\frac{h}{7})$

Step 4

Simplify the left side.

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Step 4.1

Combine $\frac{π}{3}$ and $t$ .

$\frac{π t}{3} = \arccos (\frac{h}{7})$

Step 5

Multiply both sides of the equation by $\frac{3}{π}$ .

$\frac{3}{π} \cdot \frac{π t}{3} = \frac{3}{π} \arccos (\frac{h}{7})$

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 $\frac{3}{π} \cdot \frac{π t}{3}$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{3}{π} \cdot \frac{π t}{3} = \frac{3}{π} \arccos (\frac{h}{7})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{π} (π t) = \frac{3}{π} \arccos (\frac{h}{7})$

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 $π t$ .

$\frac{1}{π} (π (t)) = \frac{3}{π} \arccos (\frac{h}{7})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{π} (π t) = \frac{3}{π} \arccos (\frac{h}{7})$

Step 6.1.1.2.3

Rewrite the expression.

$t = \frac{3}{π} \arccos (\frac{h}{7})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Combine $\frac{3}{π}$ and $\arccos (\frac{h}{7})$ .

$t = \frac{3 \arccos (\frac{h}{7})}{π}$