Question

What is $\tan 180°$?

Answer 1

The trigonometric ratio of an angle:

In trigonometry, $\tan$ of an angle is the ratio of the $\mathrm{sine}$ and $\mathrm{cosine}$ of the same angle.

$\mathbf{tan\theta }\mathbf{=}\frac{\mathbf{sin\theta }}{\mathbf{cos\theta }}$

$$\begin{gathered} \therefore \tan 180°=\frac{\sin 180°}{\cos 180°} \\ \Rightarrow =\frac{0}{-1}\left[\because \sin 180°=0\mathrm{and}\cos 180°=-1\right] \\ \Rightarrow =0 \end{gathered}$$

Hence, $\mathbf{tan}\mathbf{}\mathbf{180}\mathbf{°}$is equal to $\mathbf{0}$.