Precalculus Examples

$\sin (x) = \frac{b}{2 \sqrt{13}}$

Step 1

Simplify $\frac{b}{2 \sqrt{13}}$ .

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Step 1.1

Multiply $\frac{b}{2 \sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\sin (x) = \frac{b}{2 \sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{b}{2 \sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\sin (x) = \frac{b \sqrt{13}}{2 \sqrt{13} \sqrt{13}}$

Step 1.2.2

Move $\sqrt{13}$ .

$\sin (x) = \frac{b \sqrt{13}}{2 (\sqrt{13} \sqrt{13})}$

Step 1.2.3

Raise $\sqrt{13}$ to the power of $1$ .

$\sin (x) = \frac{b \sqrt{13}}{2 ({\sqrt{13}}^{1} \sqrt{13})}$

Step 1.2.4

Raise $\sqrt{13}$ to the power of $1$ .

$\sin (x) = \frac{b \sqrt{13}}{2 ({\sqrt{13}}^{1} {\sqrt{13}}^{1})}$

Step 1.2.5

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

$\sin (x) = \frac{b \sqrt{13}}{2 {\sqrt{13}}^{1 + 1}}$

Step 1.2.6

Add $1$ and $1$ .

$\sin (x) = \frac{b \sqrt{13}}{2 {\sqrt{13}}^{2}}$

Step 1.2.7

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

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Step 1.2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\sin (x) = \frac{b \sqrt{13}}{2 {(13^{\frac{1}{2}})}^{2}}$

Step 1.2.7.2

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

$\sin (x) = \frac{b \sqrt{13}}{2 \cdot 13^{\frac{1}{2} \cdot 2}}$

Step 1.2.7.3

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

$\sin (x) = \frac{b \sqrt{13}}{2 \cdot 13^{\frac{2}{2}}}$

Step 1.2.7.4

Cancel the common factor of $2$ .

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Step 1.2.7.4.1

Cancel the common factor.

$\sin (x) = \frac{b \sqrt{13}}{2 \cdot 13^{\frac{2}{2}}}$

Step 1.2.7.4.2

Rewrite the expression.

$\sin (x) = \frac{b \sqrt{13}}{2 \cdot 13^{1}}$

Step 1.2.7.5

Evaluate the exponent.

$\sin (x) = \frac{b \sqrt{13}}{2 \cdot 13}$

Step 1.3

Multiply $2$ by $13$ .

$\sin (x) = \frac{b \sqrt{13}}{26}$

Step 2

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

$x = \arcsin (\frac{b \sqrt{13}}{26})$