Trabajo de minimos cuadrados

1. NOMBRE: WILLIAM CLAUDIO ALANOCA CHIQUE CODIGO 2016-101010
ANGULO ∆(∗ 10−6
) ∆2
(∗ 10−12
) LOGARITMO ( Sen angulo )
23° 44’ 45’’ 4.78 22.85 -0.3950398047
42° 19’ 14’’ 2.31 5.34 -0.1718056912
44° 52’ 03’’ 2.12 4.49 -0.1515216566
69° 04’ 23’’ 0.80 0.64 -0.02963610194
39° 37’ 50’’ 2.54 6.45 -0.1952917827
26° 25’ 56’’ 4.24 17.98 -0.3515045076
75° 12’ 19’’ 0.56 0.31 -0.01464228427
38° 44’ 10’’ 2.62 6.86 -0.2036099658
∑ = 360° 00’ 40’’ ∑ =64.92 ∑ =-0.7564955283 ∑ =-0.7565562665
△= Diferencia de logsen∢i ,en el sexto decimal, al variar el ángulo en segundo.
CALCULOS:
E1 = 360 − (∑ ángulos) = 360° − 360° 00′
40′′ = −00° 00′
40′′
E2 = (∢5 + ∢6) − (∢1 + ∢2) = (39° 37’ 50’’ + 26° 25’ 56’’)− (23° 44’ 45’’ + 42° 19’ 14’’)
= 66° 03’ 46’’ − 66° 03’ 59’’ = −00° 00′
13′′
1
8
2
7
6
5
4
3

2. E3 = (∢7 + ∢8) − (∢3 + ∢4) = (75° 12’ 19’’ + 38° 44’ 10’’) − (44° 52’ 03’’ + 69° 04’ 23’’)
= 113° 56’ 29’’ − 113° 56’ 26’’ = +00° 00′
03′′
E4 = |∑ LOGARITMO (SEN ∢ IMPAR)| − |∑ LOGARITMO (SEN ∢ PAR)|
= 0.7564955283 − 0.7565562665 = −6.07 ∗ 10−5
= −60.7 ∗ 10−6
D1 = (△1−△2)+ (△3−△4)+ (△5−△6)+ (△7−△8)
= (4.78 − 2.31) + (2.12 − 0.80) + (2.54 − 4.24) + (0.56 − 2.62) = 0.03 ∗ 10−6
D2 = (△1−△2) − (△5−△6) = (4.78 − 2.31)− (2.54 − 4.24) = 4.17 ∗ 10−6
D3 = (△3−△4)− (△7−△8) = (2.12 − 0.80) − (0.56 − 2.62) = 3.38 ∗ 10−6
D4 = ∑ ∆2
= 64.92
A =
E1D1
8
+
E2 D2
4
+
E3D3
4
=
(−40′′)(−0.03)
8
+
(−13′′)(4.17)
4
+
(+03′′)(3.38)
4
= −16.021 ∗ 10−6
B =
D1
2
8
+
D2
2
4
+
D3
2
4
=
−0.032
8
+
4.172
4
+
3.382
4
= 7.203 ∗ 10−12
K4 =
E4 − A
D4 − B
=
(−60.7 − (−16.021))
(64.92 − 7.203)
=
8.985
58.314
= −0.774 ∗ 106
K3 =
E3 − K4D3
4
=
(+03′′)− (−0.774)(3.38)
4
= −1.404
K2 =
E2 − K4D2
4
=
(−13′′)− (−0.774)(4.17)
4
= −2.443
K1 =
E1 − K4D1
8
=
(−40′′)− (−0.774)(0.03)
8
= −4.997
CORRECCIONES:
V1 = K1 + K2 +△1 K4 = (−4.997)+ (−2.443)+ (4.78)(−0.774) = −𝟏𝟏. 𝟏𝟑𝟗
V2 = K1 + K2 −△2 K4 = (−4.997) + (−2.443) − (2.31)(−0.774) = −𝟓. 𝟔𝟓𝟐
V3 = K1 + K3 +△3 K4 = (−4.997) + (−1.404) + (2.12)(−0.774) = −𝟒. 𝟕𝟔𝟎
V4 = K1 + K3 −△4 K4 = (−4.997) + (−1.404) − (0.80)(−0.774) = −𝟒. 𝟐𝟏𝟐
V5 = K1 − K2 +△5 K4 = (−4.997) − (−2.443) + (2.54)(−0.774) = +𝟒. 𝟓𝟏𝟗
V6 = K1 − K2 −△6 K4 = (−4.997) − (−2.443) − (4.24)(−0.774) = +𝟎. 𝟕𝟐𝟖
V7 = K1 − K3 +△7 K4 = (−4.997) − (−1.404) + (0.56)(−0.774) = −𝟒. 𝟎𝟐𝟔
V8 = K1 − K3 −△8 K4 = (−4.997) − (−1.404) − (2.62)(−0.774) = −𝟏. 𝟓𝟔5
ANGULOS CORREGIDOS:

3. ANGULO 1 = ∢1 ± V1 = 23° 44’ 45’’ − 00° 00′
11.139′′
= 23° 44′
33.86′′
ANGULO 2 = ∢2 ± V2 = 42° 19’ 14’′ − 00° 00′
5.652′′
= 42° 19′
08.35′′
ANGULO 3 = ∢3 ± V3 = 44° 52’ 03’’ − 00° 00′
4.760′′
= 44° 51′
58.24′′
ANGULO 4 = ∢4 ± V4 = 69° 04’ 23’’ − 00° 00′
4.212′′
= 69° 04′
18.79′′
ANGULO 5 = ∢5 ± V5 = 39° 37’ 50’’ + 00° 00′
4.519′′ = 39° 37′
54.52′′
ANGULO 6 = ∢6 ± V6 = 26° 25’ 56’’ + 00° 00′
0.728′′ = 26° 25′
56.73′′
ANGULO 7 = ∢7 ± V7 = 75° 12’ 19’’ − 00° 00′
4.026′′
= 75° 12′
14.97′′
ANGULO 8 = ∢8 ± V8 = 38° 44’ 10’’ − 00° 00′
1.565′′
= 38° 44′
08.43′′
𝑆𝑈𝑀𝐴 = 360° 00′
13.89′′
REDONDEANDO VALORES
ANGULO 1 = 23° 44′
34′′
ANGULO 2 = 42° 19′
08′′
ANGULO 3 = 44° 51′
58′′
ANGULO 4 = 69° 04′
19′′
ANGULO 5 = 39° 37′
55′′
ANGULO 6 = 26° 25′
57′′
ANGULO 7 = 75° 12′
15′′
ANGULO 8 = 38° 44′
08′′