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irina1246 [14]
3 years ago
10

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 funct

ion?
Mathematics
2 answers:
Musya8 [376]3 years ago
7 0
\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}}
12345 [234]3 years ago
6 0
The answer is 5 square root 61 divided by 61
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