Find the Sine (0.09,0.12)

$(0.09, 0.12)$

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(0.09, 0.12)$ , draw the triangle between the three points $(0, 0)$ , $(0.09, 0)$ , and $(0.09, 0.12)$ .

Opposite : $0.12$

Adjacent : $0.09$

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

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Raise $0.09$ to the power of $2$ .

$\sqrt{0.0081 + {(0.12)}^{2}}$

Raise $0.12$ to the power of $2$ .

$\sqrt{0.0081 + 0.0144}$

Add $0.0081$ and $0.0144$ .

$\sqrt{0.0225}$

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{0.12}{\sqrt{0.0225}}$ .

$\frac{0.12}{\sqrt{0.0225}}$

Simplify $\sin (θ)$ .

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Multiply $\frac{0.12}{\sqrt{0.0225}}$ by $\frac{\sqrt{0.0225}}{\sqrt{0.0225}}$ .

$\sin (θ) = \frac{0.12}{\sqrt{0.0225}} \cdot \frac{\sqrt{0.0225}}{\sqrt{0.0225}}$

Combine and simplify the denominator.

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Multiply $\frac{0.12}{\sqrt{0.0225}}$ and $\frac{\sqrt{0.0225}}{\sqrt{0.0225}}$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{\sqrt{0.0225} \sqrt{0.0225}}$

Raise $\sqrt{0.0225}$ to the power of $1$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{\sqrt{0.0225} \sqrt{0.0225}}$

Raise $\sqrt{0.0225}$ to the power of $1$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{\sqrt{0.0225} \sqrt{0.0225}}$

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

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{\sqrt{0.0225}}^{1 + 1}}$

Add $1$ and $1$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{\sqrt{0.0225}}^{2}}$

Rewrite ${\sqrt{0.0225}}^{2}$ as $0.0225$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.0225}$ as ${0.0225}^{\frac{1}{2}}$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{({0.0225}^{\frac{1}{2}})}^{2}}$

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

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{0.0225}^{\frac{1}{2} \cdot 2}}$

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

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{0.0225}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{{0.0225}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{0.0225}$

Evaluate the exponent.

$\sin (θ) = \frac{0.12 \sqrt{0.0225}}{0.0225}$

Multiply $0.12$ by $\sqrt{0.0225}$ .

$\sin (θ) = \frac{0.018}{0.0225}$

Divide $0.018$ by $0.0225$ .

$\sin (θ) = 0.8$

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