Question

The value of \[\tan 0{}^\circ \] is:
a). 0
b). $\dfrac{1}{2}$
c). $\dfrac{\sqrt{3}}{2}$
d). 1

Answer 1

Hint: To find the value of \[\tan 0{}^\circ \]we will either use the standard trigonometric table and then get the value of \[\tan 0{}^\circ \] by it directly or we can find its value by just using the property $\tan \theta =\dfrac{\sin \theta }{\cos \theta }$ and then put $0{}^\circ $ in place of $\theta $ in the above equation. And, since we all know that $\sin 0{}^\circ =0$ and $\cos 0{}^\circ =1$ we will then use them to get the value of \[\tan 0{}^\circ \].

Complete step by step answer:
We can see that the above given question is a simple question of trigonometry in which we are asked to find the value of \[\tan 0{}^\circ \]. We all know that the value of \[\tan 0{}^\circ \] is present in the standard trigonometric table and it is equal to 0. But if we do not know its value or want to find it, we will use the property that $\tan \theta =\dfrac{\sin \theta }{\cos \theta }$ .
Now, after replacing $\theta $ by $0{}^\circ $from $\tan \theta =\dfrac{\sin \theta }{\cos \theta }$, we will get:
$\tan 0{}^\circ =\dfrac{\sin 0{}^\circ }{\cos 0{}^\circ }$
Now, we all know that $\sin 0{}^\circ =0$ and $\cos 0{}^\circ =1$, so after replacing $\sin 0{}^\circ $ by 0 and $\cos 0{}^\circ $ by 1 in$\tan 0{}^\circ =\dfrac{\sin 0{}^\circ }{\cos 0{}^\circ }$, in we will get:
$\tan 0{}^\circ =\dfrac{0}{1}=0$
So, we can say that $\tan 0{}^\circ =0$.

So, the correct answer is “Option a”.

Note: Students are required to note that the tangent function is the function of sine and cosine function and its value can be obtained by dividing the sine function by cosine function with their respective degree values. Also, students must note that whenever cosine function value becomes zero then tangent function becomes undefined.