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# Basic Trigonometric Ratios

### Trigonometric relationships

• There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent.
• These six trigonometric ratios are abbreviated as $$\sin$$, $$\cos$$, $$\tan$$, $$\csc$$, $$\sec$$, $$\cot$$.
• These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle $$\theta$$.

• Using the triangle above:
\begin{eqnarray*}
\sin\theta &=& \frac{\mbox{Opposite}}{\mbox{Hypothenuse}}\\
\tan\theta &=& \frac{\mbox{Opposite}}{\mbox{Adjacent}} = \frac{\sin\theta}{\cos\theta} \\
\csc\theta &=& \frac{1}{\sin\theta} \\
\sec\theta &=& \frac{1}{\cos\theta} \\
\cot\theta &=& \frac{1}{\tan\theta}= \frac{\cos\theta}{\sin\theta}
\end{eqnarray*}