Question

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

Answer 1

Hint: 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.