Question

Express the following angles into radians.
(i) 50° 37' 30"
(ii) -10°40' 30"

Answer 1

Answer:

9π/32

-373π/7200

Step-by-step explanation:

We know that,

1° = 60'                    180° = π

1 ' = 1°/60                 1° = π/180

(i) 50° 37' 30"

Step 1

30'' = (1'/2)

Step 2

37'30'' =37'+(1'/2)= 74'+1'/2 = 75°/2(60) = 5°/8

Step 3

50° 37' 30" =( (50(8))+5°/)8  = 405°/8

Step 4

405°/8 * (π/180°) = 9π/32

(ii) -10°40' 30"

Step 1

30'' = (1'/2)

Step 2

40'30'' =40'+ (1'/2)= 80'+1' /2 = 81/2(60) = 27°/40

Step 3

-10°40'30" =( -10°) + 27/40 = -373°/40

Step 4

-373/40 * (π/180°) = -373π/7200