Question

Evaluate the value of $\tan 270$ ?

Answer 1

Hint: Here in this question we have been asked to evaluate the value of $\tan {{270}^{\circ }}$ . For answering this question we will use the valid conversion given as $\tan \left( {{180}^{\circ }}+\theta \right)=\tan \theta $ and the value given as $\tan {{90}^{\circ }}$ is undefined.

Complete step by step answer:
Now considering the question we have been asked to evaluate the value of $\tan {{270}^{\circ }}$ . For answering this question we will use the valid conversion given as $\tan \left( {{180}^{\circ }}+\theta \right)=\tan \theta $which we have learnt during the basics of trigonometry.
From the basic concepts of trigonometry we have learnt about a table specifying the values of all trigonometric values corresponding to specific values of angles. From that table we have $\tan {{90}^{\circ }}$ is undefined.
Now we can say that $\tan {{270}^{\circ }}=\tan \left( {{180}^{\circ }}+{{90}^{\circ }} \right)=\tan {{90}^{\circ }}$ . Hence we can conclude that the value of $\tan {{270}^{\circ }}$ is undefined.

Note: During the process of answering questions of this type we should be sure with the calculations that we perform in between the steps and the trigonometric concepts that we apply in between. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. Alternatively this question can be answered by using the valid conversion given as $\begin{align}
  & \tan \left( {{270}^{\circ }} \right)=\dfrac{\sin \left( {{270}^{\circ }} \right)}{\cos \left( {{270}^{\circ }} \right)} \\
 & \Rightarrow \dfrac{\sin \left( {{180}^{\circ }}+{{90}^{\circ }} \right)}{\cos \left( {{180}^{\circ }}+{{90}^{\circ }} \right)}=\dfrac{-\sin {{90}^{\circ }}}{-\cos {{90}^{\circ }}} \\
 & \Rightarrow \dfrac{1}{0}=undefined \\
\end{align}$
which will also lead to ending up having the same conclusion. Hence we can say that we will get the correct answer with any correct method.