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

the answer is 5 square root 61 divided by 61

Answer 2

`\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=√(a^2+b^2)\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=√((-6)^2+(5)^2)\implies c=√(36+25)\implies \boxed{c=√(61)} \\\\\\ sin(\theta)=\cfrac{5}{√(61)}`

now, let's rationalize the denominator


`\bf \cfrac{5}{√(61)}\cdot \cfrac{√(61)}{√(61)}\implies \cfrac{5√(61)}{(√(61))^2}\implies \boxed{\cfrac{5√(61)}{61}}`