Question

Find the reference angle in degrees and radians 120 degrees.

Answer 1

Hint: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.