Question

Find the reference angle in degrees and radians 120 degrees.

Answer 1

The reference angle is the angle between the terminal arm of the angle and the “x” axis always larger than zero degrees and smaller that each degree is divided into ${60^ \circ }$ equal minutes and each minute is further divided into equal $60$ seconds. The relation between degree and radian is given by the formula, ${1^ \circ } = \dfrac{\pi }{{180}}$ where $\pi$ a constant is whose value is approximately equal to$3.14$.

Complete step by step answer:
Since, 120 degrees is in quadrant 2, the reference angle represented by $\theta$can be found by solving the equation$120 + \theta = 180$. Hence we can have the value of $\theta$ from the equation as $60$ by subtracting $180$ from $120$.
To convert this to radians we multiply by the ratio$\dfrac{\pi }{{180}}$.
Hence we have,
$60 \times \dfrac{\pi }{{180}}$
We can have $180$ cancelling $60$ and become a $3$ in the denominator.This leaves us with $\dfrac{\pi }{3}$ radians, which is our reference angle in radians.

Note: Students may go wrong while converting the value from degree to radian, is that they might think that both $\pi$ and ${180^ \circ }$ are same in this instance as although we use both for same purpose as in angular form $\pi$ is considered as ${180^ \circ }$ but not here, here we need the value of $\pi$ which is $3.1415$ so they won’t cut themselves to reduced value of 1. The radian measure corresponding to the degree measure is obtained after converting them into radian by multiplying them with $\dfrac{\pi }{{180}}$.The reference angle represented by $\theta$ can be found by solving the equation $120 + \theta = 180$ when in quadrant two.