Question

Express each of the following angles in degrees.

(i) (5π/12)^c

(ii) -(18π/5)^c

(iii) (5/6)^c

(iv) (-4)^c

Answer 1

We know that.

(i) Angle in degrees = 5π/ 12 x 180/π = 75

(ii) Angle in degrees = -18π/5 x 180/π = -648

(iii) Angle in degrees = 5/6 x 180/π = 47.7272°

Write Angle in degrees, minutes and second:

We know,

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

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

Therefore, 0.7272° = 0.7272 x 60′ = 43.632′

Angle in seconds = 0.632 x 60” = 37.92” or 38”

Final angle = 47° 43′ 38”

(iv) Angle in degrees = -4 x 180/π = = -229.0909°

Write Angle in minutes:

We know,

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

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

Therefore, 0.0909° = 0.0909 x 60′ = 5.4545′

Angle in seconds = 0.4545 x 60” = 27.27”

Final angle = -(229° 5′ 27”)