Trig Ratios

The whole point of trig is the ratios of the sides of right triangles. As long as the triangles are proportional, the ratios will always be the same.

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The two triangles above are similar. That means that the larger one is the same exact shape, but each side is twice as large.

{\renewcommand{\arraystretch}{2}
\begin{tabular}{c | c}

Small triangle & Big triangle\\ \hline

\sin(\theta)=\frac{3}{5} & \sin(\theta)=\frac{6}{10}= \hspace{1.5cm} \\

\cos(\theta)=\frac{4}{5} & \cos(\theta)=\frac{8}{10}=\hspace{1.5cm}\\

\tan(\theta)=\frac{3}{4} & \tan(\theta)=\frac{6}{8}=\hspace{1.5cm}

\end{tabular}} \quad

Since the lengths of the sides are proportional (multiplied by 2), the trig ratios are the same. \\

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{\renewcommand{\arraystretch}{2}
\begin{tabular}{c | c}

Small triangle & Big triangle\\ \hline

\sin(20^\circ)=\frac{y}{z} & \sin(20^\circ)=\frac{2y}{2z}= \hspace{1.5cm} \\

\cos(20^\circ)=\frac{x}{z} & \cos(20^\circ)=\frac{2x}{2z}=\hspace{1.5cm}\\

\tan(20^\circ)=\frac{y}{x} & \tan(20^\circ)=\frac{2y}{2x}=\hspace{1.5cm}

\end{tabular}} \quad