CONVERT DEGREES MINUTES SECONDS TO RADIANS

Find the radian measures of the corresponding to the following degree measures.

Problem 1 :

37° 30'

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

30 minutes = 30/60 = 1/2 degrees

Combining degrees :

= 37 + 1/2

= (74+1)/2

= (75/2)°

Converting degrees to radian, we get

= (75/2) ⋅ (π/180)

= 5π/24

Problem 2 :

5° 37' 30''

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

37 minutes = 37/60 degrees

30 seconds = 30/3600 degree

Combining degrees :

Problem 3 :

40° 20'

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

20 minutes = 20/60 = 1/3 degrees

Combining degrees :

= 40 + 1/3

= (120+1)/3

= (121/3)°

Converting degrees to radian, we get

= (121/3) ⋅ (π/180)

= 121π/540

Problem 4 :

75° 6' 30''

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

6 minutes = 6/60 degrees = 1/10

30 seconds = 30/3600 degree = 1/120

Combining degrees :

Problem 5 :

7° 30'

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

30 minutes = 30/60 = 1/2 degrees

Combining degrees :

= 7 + 1/2

= (14+1)/2

= (15/2)°

Converting degrees to radian, we get

= (15/2) ⋅ (π/180)

= π/24

Problem 6 :

125° 30'

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

30 minutes = 30/60 = 1/2 degrees

Combining degrees :

= 125 + 1/2

= (250+1)/2

= (251/2)°

Converting degrees to radian, we get

= (251/2) ⋅ (π/180)

= 251π/360

Problem 7 :

-47° 30'

Solution :

Converting minutes to degrees :

1 minute = 1/60 degree

30 minutes = 30/60 = 1/2 degrees

Combining degrees :

= -(47 + 1/2)

= -(94+1)/2

= -(95/2)°

Converting degrees to radian, we get

= -(95/2) ⋅ (π/180)

= -19π/72