Express each of the following angles in degrees. (i) 5π/12

Question

Express each of the following angles in degrees.

(i) \(\frac{5\pi}{12}\)

(ii) - \(\frac{18\pi}{5}\)

(iii) \(\frac{5}{5}\)

(iv) -4

Answer 1

(i) Formula : Angle in degrees = Angle in degrees × \(\frac{\pi}{180}\)

Therefore, Angle in degrees = \(\frac{5\pi}{12}\) x \(\frac{180}{\pi}\) = 75°

(ii) Formula : Angle in degrees = Angle in radians x \(\frac{180}{\pi}\)

Therefore, Angle in degrees = - \(\frac{18\pi}{5}\) x \(\frac{180}{\pi}\) = - 648°

(iii) Formula : Angle in degrees = Angle in degrees × \(\frac{180}{\pi}\)

The angle in minutes = Decimal of angle in radian x 60.’ 

The angle in seconds = Decimal of angle in minutes x 60.’’

Therefore, Angle in degrees = \(\frac{5}{6}\) x \(\frac{180}{\pi}\) = \(\frac{150}{\frac{22}7}\) = 47.7272°

Angle in minutes = 0.7272 x 60' = 43.632'

Angle in seconds = 0.632 x 60" = 37.92"

Final angle = 47° 43' 38"

(iv) Formula : Angle in degrees = Angle in radians x \(\frac{180}{\pi}\)

The angle in minutes = Decimal of angle in radian x 60.’ 

The angle in seconds = Decimal of angle in minutes x 60.’’

Therefore, Angle in degrees = - 4 x \(\frac{180}{\pi}\) = - \(\frac{150}{\frac{22}7}\) = - 229.0909°

Angle in minutes = 0.0909 x 60' = 5.4545'

Angle in seconds = 0.4545 x 60" = 27.27"

Final angle = - 229° 5' 27"

Answer 2

D=\({180}\over{\pi} \)*R 

where D is angle in degree and R is angle in radians

(i)5\({\pi}\over12 \)=\({180}\over{\pi} \)*5\({\pi}\over12 \)=15*5=75º

(ii)-18\({\pi}\over5\)=\({180}\over{\pi} \)*(-18\({\pi}\over5\))=-648º

(iii)5/5=i radian=180/\(\pi \)º

(iv)-4=\({180}\over{\pi} \)*4=720/\(\pi \)º