Question

A nick on the edge of a CD rotates to (−6, 5) during one song when represented graphically. What is the sine value of this function?

Answer 1

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\\\\ -------------------------------\\\\ \begin{array}{rllll} (-6&,&5)\\ \uparrow &&\uparrow \\ a&&b\\ x&&y \end{array}\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-6)^2+(5)^2}\implies c=\sqrt{36+25}\implies \boxed{c=\sqrt{61}} \\\\\\ sin(\theta)=\cfrac{5}{\sqrt{61}}$

now, let's rationalize the denominator

$\bf \cfrac{5}{\sqrt{61}}\cdot \cfrac{\sqrt{61}}{\sqrt{61}}\implies \cfrac{5\sqrt{61}}{(\sqrt{61})^2}\implies \boxed{\cfrac{5\sqrt{61}}{61}}$

Answer 2

The answer is 5 square root 61 divided by 61