1° = 60 minutes = 60'
1 minute = 60 seconds = 60''
To convert 1 minute to degree, we have to multiply the given minute by 1/60
To convert 1 second to degree, we have to multiply the given minute by 1/3600
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
Sep 22, 23 08:41 AM
Sep 22, 23 06:13 AM
Sep 22, 23 06:09 AM