Question

What is opposite and reciprocal of 2pi?

Answer 1

Hint: Given the angle is radians. We have to find the opposite angle and the reciprocal also. Reciprocal is just the same value written in the form of fraction with 1 as numerator and the value (here the angle) in the denominator. And the opposite angle is the same angle but with a negative sign.

Complete step by step solution:
Given that the angle is \[2\pi \] .
Now if x is any number then the reciprocal of the number is given by the fraction of the form \[\dfrac{1}{x}\].
Here the given is an angle in radians that is \[2\pi \] .
Now the reciprocal of the given angle is \[\dfrac{1}{{2\pi }}\].
The opposite angel is given by \[ - 2\pi \].
Thus, the opposite and reciprocal of the given angle is \[ - \dfrac{1}{{2\pi }}\]

Note: Note that whether the angle is in radians or degrees the way of writing the reciprocal and opposite remains the same. Minus sign is from the way of the number line. In which the numbers on right of origin are positive and those on the left are negative.