If π = \(\frac{22}{7}\), then a unit radian is approximately equal to

1.	If π = \(\frac{22}{7}\), then a unit radian is approximately equal to(a) 57° 16′ 22′′ (b) 57° 15′ 22′′ (c) 57° 16′ 20′′ (d) 57° 15′ 20′'
Answer» (a) 57° 16′ 22′′ π radians = 180° ⇒ 1 radian = \(\frac{180}{π} \) degree = \(\frac{180}{22}\times7 \) degree = \(\frac{630}{11}\)degree = \(57\frac{3}{11}\) degree = 57° + \(\frac{3}{11}\times60\) min = 57° + \(\frac{180}{11}\) min = 57° + 16\(\frac4{11}\) = 57°+ 16' + \(\frac4{11}\) x 60 s = 57° + 16′ + 21.8′′ = 57° 16′ 22′′ (approx).

If π = \(\frac{22}{7}\), then a unit radian is approximately equal to(a) 57° 16′ 22′′ (b) 57° 15′ 22′′ (c) 57° 16′ 20′′ (d) 57° 15′ 20′'

Answer»

(a) 57° 16′ 22′′

π radians = 180°

⇒ 1 radian = \(\frac{180}{π} \) degree = \(\frac{180}{22}\times7 \) degree

= \(\frac{630}{11}\)degree = \(57\frac{3}{11}\) degree

= 57° + \(\frac{3}{11}\times60\) min = 57° + \(\frac{180}{11}\) min

= 57° + 16\(\frac4{11}\)

= 57°+ 16' + \(\frac4{11}\) x 60 s

= 57° + 16′ + 21.8′′

= 57° 16′ 22′′ (approx).