Basic Math Examples

$h = 7 \sin (\frac{π}{21} t) + 28$

Step 1

Rewrite the equation as $7 \sin (\frac{π}{21} t) + 28 = h$ .

$7 \sin (\frac{π}{21} t) + 28 = h$

Step 2

Subtract $28$ from both sides of the equation.

$7 \sin (\frac{π}{21} t) = h - 28$

Step 3

Divide each term in $7 \sin (\frac{π}{21} t) = h - 28$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 \sin (\frac{π}{21} t) = h - 28$ by $7$ .

$\frac{7 \sin (\frac{π}{21} t)}{7} = \frac{h}{7} + \frac{- 28}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 \sin (\frac{π}{21} t)}{7} = \frac{h}{7} + \frac{- 28}{7}$

Step 3.2.1.2

Divide $\sin (\frac{π}{21} t)$ by $1$ .

$\sin (\frac{π}{21} t) = \frac{h}{7} + \frac{- 28}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 28$ by $7$ .

$\sin (\frac{π}{21} t) = \frac{h}{7} - 4$

Step 4

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

$\frac{π}{21} t = \arcsin (\frac{h}{7} - 4)$

Step 5

Simplify the left side.

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Step 5.1

Combine $\frac{π}{21}$ and $t$ .

$\frac{π t}{21} = \arcsin (\frac{h}{7} - 4)$

Step 6

Multiply both sides of the equation by $\frac{21}{π}$ .

$\frac{21}{π} \cdot \frac{π t}{21} = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $\frac{21}{π} \cdot \frac{π t}{21}$ .

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Step 7.1.1.1

Cancel the common factor of $21$ .

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Step 7.1.1.1.1

Cancel the common factor.

$\frac{21}{π} \cdot \frac{π t}{21} = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{π} (π t) = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7.1.1.2

Cancel the common factor of $π$ .

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Step 7.1.1.2.1

Factor $π$ out of $π t$ .

$\frac{1}{π} (π (t)) = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{π} (π t) = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7.1.1.2.3

Rewrite the expression.

$t = \frac{21}{π} \arcsin (\frac{h}{7} - 4)$

Step 7.2

Simplify the right side.

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Step 7.2.1

Combine $\frac{21}{π}$ and $\arcsin (\frac{h}{7} - 4)$ .

$t = \frac{21 \arcsin (\frac{h}{7} - 4)}{π}$

Step 8

Simplify the numerator.

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Step 8.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$t = \frac{21 \arcsin (\frac{h}{7} - 4 \cdot \frac{7}{7})}{π}$

Step 8.2

Combine $- 4$ and $\frac{7}{7}$ .

$t = \frac{21 \arcsin (\frac{h}{7} + \frac{- 4 \cdot 7}{7})}{π}$

Step 8.3

Combine the numerators over the common denominator.

$t = \frac{21 \arcsin (\frac{h - 4 \cdot 7}{7})}{π}$

Step 8.4

Multiply $- 4$ by $7$ .

$t = \frac{21 \arcsin (\frac{h - 28}{7})}{π}$