Question

How do you convert $ - 120$ degrees to radians?

Answer 1

Hint: The angle $\alpha $ in radians is equal to the angle $\alpha $ in degrees times pi constant divided by $180$ degrees:
${\alpha _{(radians)}} = {\alpha _{(\deg rees)}} \times \dfrac{\pi }{{{{180}^0}}}$
Or you can say,
\[radians = \deg rees \times \dfrac{\pi }{{{{180}^0}}}\].

Complete step by step solution:
According to the given data, we need to write $\alpha $(radians) $ - 120$ degrees into radians.
For which we are going to use this formula,
${\alpha _{(radians)}} = {\alpha _{(\deg rees)}} \times \dfrac{\pi }{{{{180}^0}}}$
On substituting the data in the above given expression, we get
${\alpha _{(radians)}} = - {120^0} \times \dfrac{\pi }{{{{180}^0}}}$
$ \Rightarrow - {120^0} \times \dfrac{{3.14159}}{{{{180}^0}}} = - 2.0943951$radians

Therefore, we get that $ - {120^0}$ is equivalent to $ - 2.0943951$ radians.

Note:
Degrees to radians conversion formula is given by,
One degree is equal \[0.01745329252\] radians:
${1^0} = \dfrac{\pi }{{180}} = 0.005555556 \pi = 0.01745329252{\text{ }}rad$.