How do you convert -120 degrees to radians?

Jun 9, 2018

$- \frac{2 \pi}{3}$

Explanation:

$\text{to convert from "color(blue)"degrees to radians}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{radian measure"="degree measure } \times \frac{\pi}{180}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{radian } = - {\cancel{120}}^{2} \times \frac{\pi}{\cancel{180}} ^ 3 = - \frac{2 \pi}{3}$

Jun 9, 2018

Using $N \cdot \frac{\pi}{180}$

Explanation:

Where N is the constant (i.e. -120 degrees)

Also, $180$ degrees is equal to $\pi$ radians.

$N \cdot \frac{\pi}{180}$
$\left(- 120\right) \cdot \frac{\pi}{180} = - \frac{2}{3} \pi$

$- \frac{2 \pi}{3.}$ Explanation:

Radian is a unit for measuring angles using arcs of a circle.

By the Definition of $1$ Radian, We know,

The angle subtended at the centre of a circle by the arc equal in length with the radius of the given circle, is called $1$ Radian.

Now, We know,

In Any Circle, The ratio of the angles subtended at the centre by the various arcs of the circle is equal to the ratio of the lengths of those respective arcs.

Now, From The Picture,

$\textcolor{w h i t e}{\times x} \frac{\angle A O B}{4 \text{ right angles}} = \frac{\cancel{r}}{2 \pi \cancel{r}}$

rArr (1color(ForestGreen)(" Radian"))/(4 " right angles") = 1/(2pi)

$\Rightarrow 1 \frac{\textcolor{F \mathmr{and} e s t G r e e n}{\text{ Radian") = (cancel4^2 " right angles}}}{\cancel{2} \pi}$

$\Rightarrow 1 \frac{\textcolor{F \mathmr{and} e s t G r e e n}{\text{ Radian") = (2 " right angles}}}{\pi}$

$\Rightarrow 1 \textcolor{F \mathmr{and} e s t G r e e n}{\text{ Radian}} = {180}^{\circ} / \left(\pi\right)$

$\Rightarrow {1}^{\circ} = \frac{\pi}{180} \textcolor{F \mathmr{and} e s t G r e e n}{\text{ Radians}}$

Now, You got the Conversion Factor.

So, $- {120}^{\circ} = - {\cancel{120}}^{2} \times \frac{\pi}{\cancel{180}} ^ 3 \text{ Radians" = -(2pi)/3 " Radians}$

Hope This Helps.