Another Trigonometric Function: Tangent
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Evaluate (if possible)
i) \(\tan \dfrac{{3\pi }}{2}\)
ii) \(\tan ( - 3\pi )\)
\begin{align}
&\begin{aligned}\text{(i)}\quad \tan \frac{3 \pi}{2} &=\tan \left(\pi+\frac{\pi}{2}\right) \\ &=-\tan \frac{\pi}{2} \end{aligned}\\
&\tan \frac{\pi}{2}\ \text{not defined}\\
&\therefore\ -\tan \frac{\pi}{2}\ \text{not defined}\\
&\begin{aligned}\text{(ii)}\quad \tan (-3 \pi) &=-\tan 3 \pi \\
&=-\tan (2 \pi+\pi) \\
&=-\tan \pi \\
&=0 \end{aligned}
\end{align}
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