Question

How do you convert $$-300$$ degrees to radians?

Answer 1

Hint: Here, we will use the basic conversion factor of the degree into the radian. We will multiply the converting factor with the given value in degrees to get the value into the radians. The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.

Complete step by step solution:
The given value in degrees $$-300$$.
We know that the value of 1 degree is equal to $${\displaystyle \frac{\pi }{180}}$$ radians i.e. $$1^{\circ }={\displaystyle \frac{\pi }{180}}rad$$.
So, to convert the given value in degrees into the radians we will multiply this converting factor with the given value for its conversion into radians. Therefore, we get
$$-{300}^{\circ }=\left(-300\right)\times {\displaystyle \frac{\pi }{180}}$$ rad
Now we will simply solve this equation to get the value given in degrees in terms of the radians. Therefore, we get
$$\Rightarrow -{300}^{\circ }=-{\displaystyle \frac{5}{3}}\times \pi$$ rad
Now we will substitute the value of pi in the above equation. We know that the value of $$\pi =3.14$$. So, we will put the value of pi in the equation. Therefore, we get
$$\Rightarrow -{300}^{\circ }=-{\displaystyle \frac{5}{3}}\times 3.14$$rad
$$\Rightarrow -{300}^{\circ }=-5.23$$ rad

Hence the value of $$-300$$ degrees is equal to $$-5.23$$ rad.

Note:
In mathematics, degrees are a unit of angle measure. A full circle is divided into 360 degrees and hence, a quarter of a circle, which forms a right angle is equal to one-fourth of 360 degrees i.e. 90 degrees. A degree has a symbol ${}^{\circ }$ and hence, right angle $={90}^{\circ }$. Now, another unit to measure angles is called radian. 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.