Respuesta :
Answer:
Explanation:
To convert to radians
A31∘43′53′′, 90∘32′11′′, 57∘43′56′′
using DMS approach ; 1degree = 60minutes = 3600 seconds
1° = 60' = 3600"
And degree to radian = multiply by π/180
A) 31∘43′53′′ = 31degree + 43minutes + 53 seconds
= 31 degree + 43minutes + 53/60
= 31 degree + 43.88minutes
= 31 degree + 43.88/60 = 31.73 degree x π/180 = 0.5534radians
FOR 90∘32′11′′ = 90 degree + 32minutes + 11seconds
= 90degree + 32minutes + 11/60
= 90 degree + 32.183minutes
= 90 degree + 32.183/60 = 90.54degree x π/180
= 1.580radians
FOR 57∘43′56′′ = 57degree + 43minutes+ 56seconds
= 57degree + 43minutes + 56/60
= 57 degree + 43.93minutes
= 57degree + 43.93/60 = 57.73degree X π/180
= 1.00radians
PART B
FOR 94∘22′19′′ = 94degree + 22minutes + 19seconds
= 94degree + 22minutes + 19/60
= 94degree + 22.32minutes
= 94degree + 22.32/60
= 94.37degree X π/180 = 1.65radians
FOR 40∘54′53′′ = 40degree + 54minutes + 53seconds
= 40 degree + 54minutes + 53/60
= 40 degree + 54.88minutes = 40 degree + 54.88/60
= 40.91degree X π/180 = 0.714radians
FOR 44∘42′48′′ = 44degree + 42minutes + 48seconds
= 44degree + 42.8minutes
= 44.71degree X π/180 = 0.780radians
Answer:
A.
0.176270π rad, 0.502980π rad, 0.320735π rad
B.
0.524289π rad, 0.227304π rad, 0.248407π rad
Explanation:
We know that,
1° = 60' 180° = π
1 ' = 1°/60 1° = π/180
A.
a. 31°43'53''
Step 1
53'' = 53 * 1/60
= 53'/60
Step 2
43'53''
= 43'+53'/60
= (2580+43)/60
= 2623'/60
-------- Convert to degrees
= 2623/60 * 1/60
= 2623/3600
Step 3
31°43'53''
= 31+ 2623/3600
= (111600 + 2623)/3600
= 114223°/3600
Now, we convert to radians
= 114223/3600 * π/180°
= 0.176270π rad
b.
90°32'11''
Step 1.
11' = 11 * 1/60
= 11/60
Step 2
32'11'
= 32 + 11/60
= 1931/60
-------- Convert to degrees
= 1931/60 * 1/60
= 1931/3600
Step 3
90°31'11''
= 90 + 1931/3600
= 325931°/3600
Now we convert to radians
= 325931°/3600 * π/180°
= 0.502980π rad
c.
57°43'56''
Step 1
56' = 56 * 1/60
= 56/60
= 14/15
Step 2
43'56''
= 43 + 14/15
= 659/15
Now we convert to degrees
= 659/15 * 1/60
= 659°/900
Step 3
57°43'56''
= 57 + 659/900
= 51959/900
Now we convert to radians
= 51959°/900 * π/180°
= 0.320735π rad
B.
a.
94∘22′19′′
Step 1
19'' = 19/60
Step 2
22'19''
= 22 + 19/60
= 1339/60
Now we convert to degrees
= 1339/60 * 1/60
= 1339°/3600
Step 3
94°22'19"
= 94 + 1339/3600
= 339739°/3600
Now we convert to radians
= 339739°/3600 * π/180
= 0.524289π rad
b.
40∘54′53′′
Step 1
53" = 53/60
Step 2
54'53"
= 54'+ 53/60
= 3293/60
Now we convert to degrees
= 3293/60 * 1/60
= 3293/3600
Step 3
40°54'53"
= 40 + 3293/3600
= 147293/3600
Now we convert to radians
= 147293/3600 * π/180
= 0.227304π rad
c.
44∘42′48′
Step 1
48' = 48/69
= 4/5
Step 2
42'48"
= 42 + 4/5
=214/5
Nowz we convert to degrees
= 214/5 * 1/60
= 107/150
Step 3
44°42'48"
= 44 + 107/150
= 6707/150
Now we convert to radians
= 6707/150 * π/180
= 0.248407π rad
