Trigonometry Examples

$u = a ms i n (w t)$

Step 1

Rewrite the equation as $a ms i n w t = u$ .

$a ms i n w t = u$

Step 2

Divide each term in $a ms i n w t = u$ by $a ms i n w$ and simplify.

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Step 2.1

Divide each term in $a ms i n w t = u$ by $a ms i n w$ .

$\frac{a ms i n w t}{a ms i n w} = \frac{u}{a ms i n w}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $a$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a ms i n w t}{a ms i n w} = \frac{u}{a ms i n w}$

Step 2.2.1.2

Rewrite the expression.

$\frac{ms i n w t}{ms i n w} = \frac{u}{a ms i n w}$

Step 2.2.2

Cancel the common factor of $ms$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{ms i n w t}{ms i n w} = \frac{u}{a ms i n w}$

Step 2.2.2.2

Rewrite the expression.

$\frac{i n w t}{i n w} = \frac{u}{a ms i n w}$

Step 2.2.3

Cancel the common factor of $i$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{i n w t}{i n w} = \frac{u}{a ms i n w}$

Step 2.2.3.2

Rewrite the expression.

$\frac{n w t}{n w} = \frac{u}{a ms i n w}$

Step 2.2.4

Cancel the common factor of $n$ .

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Step 2.2.4.1

Cancel the common factor.

$\frac{n w t}{n w} = \frac{u}{a ms i n w}$

Step 2.2.4.2

Rewrite the expression.

$\frac{w t}{w} = \frac{u}{a ms i n w}$

Step 2.2.5

Cancel the common factor of $w$ .

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Step 2.2.5.1

Cancel the common factor.

$\frac{w t}{w} = \frac{u}{a ms i n w}$

Step 2.2.5.2

Divide $t$ by $1$ .

$t = \frac{u}{a ms i n w}$

Step 3

Simplify $t = \frac{u}{a ms i n w}$ .

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Step 3.1

Rewrite the expression.

$t = \frac{u}{a i n w} \frac{1}{ms}$

Step 3.2

Convert $ms$ to $s$ .

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Step 3.2.1

Convert $ms$ to $s$ .

$t = \frac{u}{a i n w} (\frac{1}{ms} \times \frac{1000 ms}{1 s})$

Step 3.2.2

Cancel the common units and simplify.

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Step 3.2.2.1

Cross cancel units.

$t = \frac{u}{a i n w} (\frac{1}{ms} \times \frac{1000 ms}{1 s})$

Step 3.2.2.2

Simplify the expression.

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Step 3.2.2.2.1

Remove the canceled units.

$t = \frac{u}{a i n w} (\frac{1}{1} \times \frac{1000}{1 s})$

Step 3.2.2.2.2

Cancel the common factor of $1$ .

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Step 3.2.2.2.2.1

Cancel the common factor.

$t = \frac{u}{a i n w} (\frac{1}{1} \times \frac{1000}{1 s})$

Step 3.2.2.2.2.2

Rewrite the expression.

$t = \frac{u}{a i n w} (1 \times \frac{1000}{1 s})$

Step 3.2.2.2.3

Multiply $\frac{1000}{1 s}$ by $1$ .

$t = \frac{u}{a i n w} \cdot \frac{1000}{1 s}$

Step 3.2.2.2.4

Rewrite the expression.

$t = \frac{u}{a i n w} (1000 \frac{1}{s})$

Step 3.3

Rewrite $\frac{1}{s}$ as $Hz$ .

$t = \frac{u}{a i n w} (1000 Hz)$

Step 3.4

Simplify.

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Step 3.4.1

Combine $\frac{u}{a i n w}$ and $1000 Hz$ .

$t = \frac{u \cdot 1000}{a i n w} Hz$

Step 3.4.2

Move $1000$ to the left of $u$ .

$t = \frac{1000 u}{a i n w} Hz$