Question

Express 1.2 radian in degree measure.

Answer 1

Hint:The given problem is related to unit conversion. To convert from radian to degree we have to multiply by either ${\displaystyle \frac{180}{\pi }}$ or ${\displaystyle \frac{180}{3.14}}$

Complete step-by-step answer:
In the question we are given an angle in radian which is 1.2 rad and we have to convert it into degrees.
Before proceeding we will first briefly say something about radian.
The radian is an S.I. unit for measuring angles and is the standard unit of angular measure used in areas of mathematics. The length of an arc of unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.
Radian describes the plain angle subtended by a circular arc as the length of arc divided by radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the magnitude in radians of such a subtend angle is equal to the ratio of the arc length to the radius of circle; that is $\theta ={\displaystyle \frac{l}{r}}$, where $\theta$ is the subtended angle in radians, l is arc length and r is radius .

Conversely, the length of the enclosed arc is equal to the radius multiplied by the magnitude of the angle in radians that is $l=r\theta$.
We are given the angle value as 1.2 radian. So, to change it into a degree we have to multiply by ${\displaystyle \frac{180}{\pi }}$.
So, we can write it as,
$1.2\times {\displaystyle \frac{180}{\pi }}={\displaystyle \frac{216}{\pi }}$ or substituting $\pi$as 3.14 we get $69.79{}^{\circ }$.
Hence, the value is $69.79{}^{\circ }$.

Note: Students should think before multiplying by either ${\displaystyle \frac{180}{\pi }}$ or ${\displaystyle \frac{180\times 7}{22}}$. The radians if are given in terms of $\pi$ should be multiplied by ${\displaystyle \frac{180}{\pi }}$ otherwise by ${\displaystyle \frac{180}{3.14}}$.Students should remember to convert from degree to radian one should multiply by ${\displaystyle \frac{\pi }{180}}$ to get the value in radians and to convert from radian to degree one should multiply by ${\displaystyle \frac{180}{\pi }}$ to get the value in degrees.