Question

How do you convert $-15\text{ degrees}$ into $\text{radians}$?

Answer 1

Hint: Here we need to know the general fact that $\pi \text{ radian}$ is equal to ${180}^{\circ }$ and by this we can find the value of $1\text{ degree}$ in the unit of $\text{radian}$and then we can multiply that with $-15$ in order to get the value of degrees in radians.

Complete step by step solution:
Here we are given that we need to convert $-15\text{ degrees}$ into $\text{radians}$
Here in this problem, the student must know the general fact which says that $\pi \text{ radian}$ is equal to ${180}^{\circ }$
Hence in the mathematical form we can write that:
${180}^{\circ }=\pi \text{ radians}$$----(1)$
Now we can find the value of $1^{\circ }$ by dividing the both sides of the equation (1) with $180$:
$$\begin{gathered} {180}^{\circ }=\pi \text{ radians} \\ {1}^{\circ }={\displaystyle \frac{\pi }{180}}\text{ radians}----(2) \end{gathered}$$
Hence we have got the value of $1^{\circ }$ in radians.
Now we know that whenever we are given the value of one item, we can get the value of $n$ items by just multiplying $n$ with the value of one item. Hence in the similar way we have got the value of one degree and we can get the value of $-15$ degrees in radian by multiplying this with $-15$
Now we can multiply the equation (2) with $\left(-15\right)$ and get:
$1^{\circ }={\displaystyle \frac{\pi }{180}}\text{ radians}$
$-{15}^{\circ }=-{\displaystyle \frac{15\pi }{180}}\text{ radians}$
Now we have got the value of $-15$ degrees in radians and now we know that $180\text{ and 15}$ have the highest common factor as $15$ so we can cancel the above fraction by $15$ and get:
$-{\displaystyle \frac{15\pi }{180}}=-{\displaystyle \frac{\pi }{12}}$
So we have got:

$-{15}^{\circ }=-{\displaystyle \frac{\pi }{12}}\text{ radians}$

Note:
In order to convert one unit into another, the student must know the conversion factor of every unit. Even if we are told to convert kilogram into milligram we must know all the basic units that $1\text{ kg}=1000\text{gm and 1gm}=1000\text{mg}$.