Question

How do you convert $ - 54$ degrees to radians?

Answer 1

Hint: In the above question, we are asked to convert degrees to radians. The easiest way to convert a degree to a radian is to understand and remember the fact that $180^\circ $ is equal to $\pi $ radians or in numerical statement $3.14$ radians. Once we know this, we can easily find out the required degrees converted into radians with the help of the formula.
For that, all we need to do is, find the concerned percentage of $180^\circ $ has been taken by the fraction and then multiply that fraction by $3.14$ radians.

Complete step-by-step solution:
When finding a radian, one must know basic calculations and terms in order to easily calculate the radians from the degrees.
We know that $180^\circ $ is equal to $\pi $ radians or in numerical statement $3.14$ radians. So, now that we are sure of this, we can try to find the value of $ - 54$ degrees, by simple calculation.
Now we have,
$ \Rightarrow 180^\circ $ as $\pi $ radians, which equals $3.14$ radians
Therefore, for $ - 54$ degrees,
$ \Rightarrow \dfrac{{ - 54 \times 3.14}}{{180}}$
Now, multiplying the numbers in the numerator, we get,
$ \Rightarrow \dfrac{{ - 169.56}}{{180}}$
Dividing the numerator with the denominator, we get,
$ \Rightarrow - 0.942$ radians

Therefore, for $ - 54$ degrees the radians that are converted and found are $ - 0.942$ radians.

Note: Degrees and radians are actually ways of measuring angles. A radian is equal to the amount an angle would have to be open to capture an arc of the circle’s circumference of equal length to the circle’s radius. Always remember that $360^\circ $ is equal to $2\pi $ radians. Degrees on the other hand are more common in general. We know that there are $360^\circ $ in a circle, $180^\circ $ in half a circle and so on.