Question

Express 1.2 rad in nearest degree measure

Answer 1

Hint: We can use the relationship between radians and degree:
$\pi $ rad = 180°
and then apply a unitary method to find the nearest degree measure of 1.2 rad.
In unitary method if a quantity A is equal x then quantity B in terms of x cane be given as:
A = x
B = $\dfrac{x}{A} \times B$

Complete step-by-step answer:
Relationship between radians ( rad ) and degree ( ° ) is given as:
$\pi $ rad = 180°
We have to calculate the value of 1.2 radians, so we will use unitary method:
$\pi $ rad = 180°
1.2 rad = ${\left( {\dfrac{{180}}{\pi } \times 1.2} \right)^ \circ }$
1.2 rad = ${\left( {\dfrac{{216}}{\pi }} \right)^ \circ }$ ___________ (1)
This can either be written in the form of pie or we can also substitute the value of pie to obtain a decimal:
$\pi = \dfrac{{22}}{7}$
Substituting this in (1), we get:
$
  {\left( {\dfrac{{216}}{\pi }} \right)^ \circ } = {\left( {\dfrac{{216 \times 7}}{{22}}} \right)^ \circ } \\
   = {68.72^ \circ } \approx {68^ \circ } \\
 $
Therefore, 1.2 rad in nearest degree measure can be written as ${\left( {\dfrac{{216}}{\pi }} \right)^ \circ }$ or 68°.

Note: In general, the direct conversion can also be carried out for the angles from radians to degrees using :
$rad = \dfrac{\pi }{{180}} \times \deg ree$
Both degree and radians are the units in which the angles can be measured.
Difference between degrees and radians lies in the fact that the angle gives the measure of the tilt whereas radian measure the angle by the distance travelled and hence is defined as the distance traveled per unit radius and is also given as (according to the definition)
\[Rad{\text{ }} = {\text{ }}\dfrac{{arc{\text{ }}of{\text{ }}length}}{{radius}}\]