Question

How many radians is 2pi?

Answer 1

Hint: We are given a question based on angle conversion. The one given to us is 2pi. We know that, when converting an angle from radians to degrees, we have to multiply the angle by \[\dfrac{{{180}^{\circ }}}{\pi }\]. Using the conversion factor, we will multiply \[2\pi \] by \[\dfrac{{{180}^{\circ }}}{\pi }\] and get the value equivalent in degrees.

Complete step-by-step solution:
According to the question given to us, we have to change the angle given in radians to degrees. When we have to convert an angle present in radians to degrees, we will have to multiply the angle by the factor \[\dfrac{{{180}^{\circ }}}{\pi }\]. The conversion process works both ways, that means we can also convert the angle present in degrees to radian by using the conversion factor \[\dfrac{\pi }{{{180}^{\circ }}}\].
We are given the angle in radians as \[2\pi \].
We have to convert it into degrees, so as stated above we will be multiplying \[2\pi \] by the conversion factor \[\dfrac{{{180}^{\circ }}}{\pi }\].
That is,
\[2\pi \times \dfrac{{{180}^{\circ }}}{\pi }\]
From the above expression, we will cancel the similar terms and we get the expression as,
\[\Rightarrow 2\times {{180}^{\circ }}\]
We will now multiply the terms as in the above expression and we get the value of the expression as,
\[\Rightarrow {{360}^{\circ }}\]
Therefore, \[2\pi \] is \[{{360}^{\circ }}\].

Note: While doing the conversion, make sure that the conversion factor is written correctly. Also, while doing the calculations, the degree and the radians should not be confused and should be represented distinctly and with proper notations.