Find the Sine Given the Point (60/61,11/61)

$(\frac{60}{61}, \frac{11}{61})$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{60}{61}, \frac{11}{61})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{60}{61}, 0)$ , and $(\frac{60}{61}, \frac{11}{61})$ .

Opposite : $\frac{11}{61}$

Adjacent : $\frac{60}{61}$

Step 2

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

Apply the product rule to $\frac{60}{61}$ .

$\sqrt{\frac{60^{2}}{61^{2}} + {(\frac{11}{61})}^{2}}$

Raise $60$ to the power of $2$ .

$\sqrt{\frac{3600}{61^{2}} + {(\frac{11}{61})}^{2}}$

Raise $61$ to the power of $2$ .

$\sqrt{\frac{3600}{3721} + {(\frac{11}{61})}^{2}}$

Apply the product rule to $\frac{11}{61}$ .

$\sqrt{\frac{3600}{3721} + \frac{11^{2}}{61^{2}}}$

Raise $11$ to the power of $2$ .

$\sqrt{\frac{3600}{3721} + \frac{121}{61^{2}}}$

Raise $61$ to the power of $2$ .

$\sqrt{\frac{3600}{3721} + \frac{121}{3721}}$

Combine the numerators over the common denominator.

$\sqrt{\frac{3600 + 121}{3721}}$

Add $3600$ and $121$ .

$\sqrt{\frac{3721}{3721}}$

Divide $3721$ by $3721$ .

$\sqrt{1}$

Any root of $1$ is $1$ .

$1$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{\frac{11}{61}}{1}$ .

$\frac{\frac{11}{61}}{1}$

Step 4

Divide $\frac{11}{61}$ by $1$ .

$\sin (θ) = \frac{11}{61}$

Step 5

Approximate the result.

$\sin (θ) = \frac{11}{61} \approx 0.18032786$

Find the Sine Given the Point (60/61,11/61)

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