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Sati [7]
3 years ago
12

What are the exact values of sin theta cos theta tan theta if (3,-4) is a point on the terminal side of theta?

Mathematics
1 answer:
malfutka [58]3 years ago
6 0
\bf (\stackrel{a}{3}~,~\stackrel{b}{-4})\impliedby \textit{now 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{3^2+(-4)^2}\implies c=\sqrt{25}\implies \boxed{c=5}

\bf -------------------------------\\\\
sin(\theta )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{hypotenuse}{5}}\qquad cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\qquad tan(\theta )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{adjacent}{3}}
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