Question

How do you evaluate $\tan {90^\circ }$?

Answer 1

In the above question we are given a trigonometric term that is $\tan {90^\circ }$ and we are asked the method to evaluate it. For evaluating this we need to keep in mind that the $\tan$ being a trigonometric component can be broken into its family components that are $\sin$ and $\cos$ components. Now having the knowledge of the value of these components at ${90^\circ }$ could help in finding the asked trigonometric term that is $\tan {90^\circ }$.

Complete step-by-step answer:
So here we are given a trigonometric term that is $\tan {90^\circ }$ and we are asked the way to evaluate this. So as we know that the $\tan$ being a trigonometric component can be broken or written into its family components that are $\sin$ and $\cos$ component that is as follows –
$\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}$
Now in the question we are asked the evaluation of the $\tan {90^\circ }$ that means the $\theta = {90^\circ }$ so if we know the values of the $\sin$and $\cos$component at the $\theta = {90^\circ }$ we could evaluate the given trigonometric term that is $\tan {90^\circ }$.
So $\sin {90^\circ } = 1$
And $\cos {90^\circ } = 0$
Also the $\tan {90^\circ }$ turns out to by using the formula as stated above that is $\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}$as follows-
$\tan {90^\circ } = \dfrac{{\sin {{90}^\circ }}}{{\cos {{90}^\circ }}}$
now putting the values of respective terms from the above we get-
$\tan {90^\circ } = \dfrac{1}{0}$
Now we know that anything divided by zero becomes infinity so similarly $\tan {90^\circ }$becomes equal to infinity that is –
$\tan {90^\circ } = \infty$
So the value of the $\tan {90^\circ }$ is equal to the $\infty$

Note: While solving such kind of the question one should know about the trigonometric components and their relationship with one another and their values at the different specified angles like ${30^\circ },{45^\circ },{60^\circ },{90^\circ },{180^\circ },{0^\circ }$ which can come into handy and vital while solving such kind of the questions also the calculations with the concentration plays a key role in getting the answers right too.