B. Primary Trigonometric Ratios for Right Triangles
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B. Primary Trigonometric Ratios for Right Triangles
Warm Up |
Review of the Primary Trigonometric Ratios
Recall, from Math 10C, the names of the primary trigonometric ratios are sine, cosine, and tangent.
Given the acute angle \(\theta\), the three primary trigonometric ratios for the right triangle \(ABC\) are:
\[\begin{align}
\sin \theta &= \frac{{{\rm{opposite}}\left( {{\rm{opp}}} \right)}}{{{\rm{hypotenuse}}\left( {{\rm{hyp}}} \right)}} \\
&= \frac{a}{c} \end{align}\]
\[\begin{align}
\cos \theta &= \frac{{{\rm{adjacent}}\left( {{\rm{adj}}} \right)}}{{{\rm{hypotenuse}}\left( {{\rm{hyp}}} \right)}} \\
&= \frac{b}{c}\end{align}\]
\[\begin{align}
\tan \theta &= \frac{{{\rm{opposite}}\left( {{\rm{opp}}} \right)}}{{{\rm{adjacent}}\left( {{\rm{adj}}} \right)}} \\
&= \frac{a}{b} \end{align}\]
\sin \theta &= \frac{{{\rm{opposite}}\left( {{\rm{opp}}} \right)}}{{{\rm{hypotenuse}}\left( {{\rm{hyp}}} \right)}} \\
&= \frac{a}{c} \end{align}\]
\[\begin{align}
\cos \theta &= \frac{{{\rm{adjacent}}\left( {{\rm{adj}}} \right)}}{{{\rm{hypotenuse}}\left( {{\rm{hyp}}} \right)}} \\
&= \frac{b}{c}\end{align}\]
\[\begin{align}
\tan \theta &= \frac{{{\rm{opposite}}\left( {{\rm{opp}}} \right)}}{{{\rm{adjacent}}\left( {{\rm{adj}}} \right)}} \\
&= \frac{a}{b} \end{align}\]
Use the acronym SOH-CAH-TOA to help remember the ratios.
Sine is Opposite over Hypoteneuse
Cosine is Adjacent over Hypoteneuse
Tangent is Opposite over Adjacent