Trigonometry Examples

$d = 0.4 \sin (1760 π t)$

Step 1

Rewrite the equation as $0.4 \sin (1760 π t) = d$ .

$0.4 \sin (1760 π t) = d$

Step 2

Divide each term in $0.4 \sin (1760 π t) = d$ by $0.4$ and simplify.

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Step 2.1

Divide each term in $0.4 \sin (1760 π t) = d$ by $0.4$ .

$\frac{0.4 \sin (1760 π t)}{0.4} = \frac{d}{0.4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.4 \sin (1760 π t)}{0.4} = \frac{d}{0.4}$

Step 2.2.1.2

Divide $\sin (1760 π t)$ by $1$ .

$\sin (1760 π t) = \frac{d}{0.4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply by $1$ .

$\sin (1760 π t) = \frac{1 d}{0.4}$

Step 2.3.2

Factor $0.4$ out of $0.4$ .

$\sin (1760 π t) = \frac{1 d}{0.4 (1)}$

Step 2.3.3

Separate fractions.

$\sin (1760 π t) = \frac{1}{0.4} \cdot \frac{d}{1}$

Step 2.3.4

Divide $1$ by $0.4$ .

$\sin (1760 π t) = 2.5 \frac{d}{1}$

Step 2.3.5

Divide $d$ by $1$ .

$\sin (1760 π t) = 2.5 d$

Step 3

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

$1760 π t = \arcsin (2.5 d)$

Step 4

Divide each term in $1760 π t = \arcsin (2.5 d)$ by $1760 π$ and simplify.

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Step 4.1

Divide each term in $1760 π t = \arcsin (2.5 d)$ by $1760 π$ .

$\frac{1760 π t}{1760 π} = \frac{\arcsin (2.5 d)}{1760 π}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1760$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1760 π t}{1760 π} = \frac{\arcsin (2.5 d)}{1760 π}$

Step 4.2.1.2

Rewrite the expression.

$\frac{π t}{π} = \frac{\arcsin (2.5 d)}{1760 π}$

Step 4.2.2

Cancel the common factor of $π$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{π t}{π} = \frac{\arcsin (2.5 d)}{1760 π}$

Step 4.2.2.2

Divide $t$ by $1$ .

$t = \frac{\arcsin (2.5 d)}{1760 π}$