
Find the reference angle in degrees and radians 120 degrees.
Answer
446.7k+ views
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.
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.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Soap bubble appears coloured due to the phenomenon class 11 physics CBSE

How is the brain protected from injury and shock class 11 biology CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

What is Environment class 11 chemistry CBSE
