Trigonometry Examples

$d = 4 \sin (8 π t)$

Step 1

Rewrite the equation as $4 \sin (8 π t) = d$ .

$4 \sin (8 π t) = d$

Step 2

Divide each term in $4 \sin (8 π t) = d$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 \sin (8 π t) = d$ by $4$ .

$\frac{4 \sin (8 π t)}{4} = \frac{d}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 \sin (8 π t)}{4} = \frac{d}{4}$

Step 2.2.1.2

Divide $\sin (8 π t)$ by $1$ .

$\sin (8 π t) = \frac{d}{4}$

Step 3

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

$8 π t = \arcsin (\frac{d}{4})$

Step 4

Divide each term in $8 π t = \arcsin (\frac{d}{4})$ by $8 π$ and simplify.

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Step 4.1

Divide each term in $8 π t = \arcsin (\frac{d}{4})$ by $8 π$ .

$\frac{8 π t}{8 π} = \frac{\arcsin (\frac{d}{4})}{8 π}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 π t}{8 π} = \frac{\arcsin (\frac{d}{4})}{8 π}$

Step 4.2.1.2

Rewrite the expression.

$\frac{π t}{π} = \frac{\arcsin (\frac{d}{4})}{8 π}$

Step 4.2.2

Cancel the common factor of $π$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{π t}{π} = \frac{\arcsin (\frac{d}{4})}{8 π}$

Step 4.2.2.2

Divide $t$ by $1$ .

$t = \frac{\arcsin (\frac{d}{4})}{8 π}$