Trigonometry Examples

$\sin (\frac{200}{10 \sqrt{481}})$

Step 1

Cancel the common factor of $200$ and $10$ .

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Step 1.1

Factor $10$ out of $200$ .

$\sin (\frac{10 \cdot 20}{10 \sqrt{481}})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $10$ out of $10 \sqrt{481}$ .

$\sin (\frac{10 \cdot 20}{10 (\sqrt{481})})$

Step 1.2.2

Cancel the common factor.

$\sin (\frac{10 \cdot 20}{10 \sqrt{481}})$

Step 1.2.3

Rewrite the expression.

$\sin (\frac{20}{\sqrt{481}})$

Step 2

Multiply $\frac{20}{\sqrt{481}}$ by $\frac{\sqrt{481}}{\sqrt{481}}$ .

$\sin (\frac{20}{\sqrt{481}} \cdot \frac{\sqrt{481}}{\sqrt{481}})$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{20}{\sqrt{481}}$ by $\frac{\sqrt{481}}{\sqrt{481}}$ .

$\sin (\frac{20 \sqrt{481}}{\sqrt{481} \sqrt{481}})$

Step 3.2

Raise $\sqrt{481}$ to the power of $1$ .

$\sin (\frac{20 \sqrt{481}}{{\sqrt{481}}^{1} \sqrt{481}})$

Step 3.3

Raise $\sqrt{481}$ to the power of $1$ .

$\sin (\frac{20 \sqrt{481}}{{\sqrt{481}}^{1} {\sqrt{481}}^{1}})$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin (\frac{20 \sqrt{481}}{{\sqrt{481}}^{1 + 1}})$

Step 3.5

Add $1$ and $1$ .

$\sin (\frac{20 \sqrt{481}}{{\sqrt{481}}^{2}})$

Step 3.6

Rewrite ${\sqrt{481}}^{2}$ as $481$ .

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{481}$ as $481^{\frac{1}{2}}$ .

$\sin (\frac{20 \sqrt{481}}{{(481^{\frac{1}{2}})}^{2}})$

Step 3.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sin (\frac{20 \sqrt{481}}{481^{\frac{1}{2} \cdot 2}})$

Step 3.6.3

Combine $\frac{1}{2}$ and $2$ .

$\sin (\frac{20 \sqrt{481}}{481^{\frac{2}{2}}})$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\sin (\frac{20 \sqrt{481}}{481^{\frac{2}{2}}})$

Step 3.6.4.2

Rewrite the expression.

$\sin (\frac{20 \sqrt{481}}{481^{1}})$

Step 3.6.5

Evaluate the exponent.

$\sin (\frac{20 \sqrt{481}}{481})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sin (\frac{20 \sqrt{481}}{481})$

Decimal Form:

$0.79068159 \dots$