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}}\\  
  \cos\theta &=& \frac{\mbox{Adjacent}}{\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*}