Question

How to find $\tan \left( { - pi} \right)$?

Answer 1

In the given question, we have been asked to calculate the exact value of a trigonometric ratio in tangent. The argument (or here, we can say the angle) of the ratio is also given. We just need to calculate the answer to the ratio. The trick here is the sign of the answer. We need to see if the negative of the angle of tangent changes the value of the ratio too or does it remain the same as in cosine’s case.

Complete step by step answer:
We have to calculate the value of $\tan \left( { - \pi } \right)$. The value of tangent inverses (sign changes from negative to positive and vice versa) when the value of angle inverses. For calculating that, we ignore the negative sign with the angle, calculate the answer, and then just attach the ignored negative sign with the answer.
Now, $\tan \left( \pi \right) = 0$

So, $\tan \left( { - \pi } \right) = - \tan \left( \pi \right) = 0$

Note: So, when there is a negative sign inside the trigonometric ratio in the tangent, we calculate the value by ignoring the negative sign, write the answer and then just attach the ignored negative sign with the answer.