|
XII
<br />Natural Trigonometrical Functions
<br />Angle. ft. 'ran, See. Come. Cote. Cosin, W91931n. Tan, See. Coast. Catg. Cosln.
<br />Q+
<br />-
<br />----
<br />° i
<br />o r
<br />o f
<br />32
<br />,5299
<br />.6240
<br />1,1792
<br />1.687
<br />1.600
<br />.84805
<br />58
<br />39
<br />.6293
<br />.8098
<br />1.2868
<br />1.589
<br />1-235
<br />.77715
<br />51
<br />10
<br />5324
<br />-6289
<br />1.1813
<br />1.878
<br />1.590
<br />.84650
<br />50
<br />10
<br />.6316
<br />.8146
<br />1.2898
<br />1,583
<br />L.228
<br />.77531
<br />50
<br />20
<br />.5348
<br />.6330
<br />1.1835
<br />1,870
<br />1.580
<br />,84405
<br />40
<br />20
<br />.6338
<br />.8195
<br />1.2929
<br />1.578
<br />L.220
<br />.77347
<br />40
<br />30.5373
<br />,63711-I8571.8611.570.84339
<br />30
<br />80.6361
<br />.8243
<br />1.296D
<br />1.572
<br />1.213
<br />.77162
<br />30
<br />40
<br />5398
<br />.6412
<br />1.1979
<br />1. SW
<br />1. 560
<br />.84182
<br />20
<br />40.6383.82921
<br />MOI
<br />1,5671.206.76977
<br />20
<br />50
<br />5422
<br />.6453
<br />1.10011.844
<br />1,550
<br />.84026
<br />10
<br />50
<br />.64G5
<br />.9342
<br />1.3022
<br />1. hfil
<br />1. 109
<br />.76791
<br />10
<br />33
<br />.5446
<br />.6494
<br />1.1924
<br />1.836
<br />1,540
<br />.83867
<br />57
<br />40
<br />.5428
<br />.8391
<br />1,3054
<br />1.556
<br />1.192
<br />-76604
<br />50
<br />10
<br />.5471
<br />.6536
<br />1.1946
<br />1.828
<br />1.530
<br />-83708
<br />50
<br />10
<br />,0450
<br />,84411.30861,5501.185
<br />.76417
<br />50
<br />20
<br />.5405
<br />.6577
<br />1.19691.8201,520
<br />•83549
<br />40
<br />20
<br />.6472
<br />.84911.3118
<br />1.545
<br />1.178
<br />.76229
<br />40
<br />30
<br />.5519
<br />.6519
<br />1.1992
<br />1 312
<br />1.511
<br />•83389
<br />30
<br />30
<br />,6494
<br />.8541
<br />1.3151
<br />1 5401.171
<br />.76041
<br />30
<br />40
<br />,5544
<br />.886E
<br />.2015
<br />1.504
<br />1.501
<br />-83228
<br />20
<br />40
<br />.6517
<br />.85911.3184
<br />1.535
<br />1.154
<br />.75851
<br />20
<br />50
<br />.5568
<br />.6703
<br />1 .2039
<br />1- 796
<br />1.492
<br />.83066
<br />10
<br />W
<br />.6539
<br />.8642
<br />1.321 i
<br />1, 5291.157
<br />.75651
<br />10
<br />34
<br />,5592.67451,20621.7881.433.8290468
<br />41
<br />.6561
<br />.8093
<br />1.32511.524
<br />1.150
<br />7547149
<br />10.5616.6787
<br />-20861.7811.473.82741
<br />50
<br />10.6583.87441,32841,5191.144.75280
<br />50
<br />20
<br />-5640.68301.21101,7731.484.82577
<br />40
<br />20.6604
<br />.87961,33181,5141.137
<br />.75083
<br />40
<br />30
<br />.5664
<br />.68731.21341.7661,455
<br />,82413
<br />30
<br />30
<br />.6626
<br />.88471.33521,5091.130
<br />.74896
<br />30
<br />40
<br />.5688
<br />.6916
<br />1,21.58
<br />1.758
<br />1.446
<br />,82248
<br />20
<br />40
<br />.6648
<br />.8899
<br />1,3386
<br />1.504
<br />1. 124
<br />.74703
<br />20
<br />50.5712.69591.21831,7511.437.82082
<br />10
<br />50.6870,89521.34211.4991,117.74509
<br />10
<br />35
<br />.5736
<br />-7003
<br />1.2208
<br />1.743
<br />1,428
<br />.81915
<br />65
<br />42
<br />.6891
<br />.9004
<br />1.3456
<br />1.494
<br />1.111
<br />,74314
<br />48
<br />10
<br />.5700
<br />.7046
<br />1.2233
<br />1.7361.419
<br />,81748
<br />50
<br />10,6713.90571:34921.4901.104.74120
<br />50
<br />20.5783.70891.22581,7291,411.81580
<br />40
<br />20.6734.91101.35271,4851.098.73924
<br />40
<br />30.5807
<br />-71331.22631,7221,402.81412
<br />30
<br />30,6755
<br />0163
<br />1.3563
<br />1.480
<br />1. 091
<br />.73723
<br />30
<br />40
<br />,5831
<br />.7177
<br />1.2309
<br />1.715
<br />1.
<br />,81242
<br />20
<br />40
<br />.6777
<br />.9217
<br />1,3600
<br />1.4751.085
<br />,73531
<br />20
<br />50
<br />.5854
<br />,7221
<br />1,2335
<br />1,708
<br />1.285
<br />.81072
<br />10
<br />50
<br />.6799
<br />.9271
<br />1.3636
<br />1,471
<br />1.079
<br />.73333
<br />10
<br />38
<br />.5878
<br />-7285
<br />1.2361
<br />1,7011,376
<br />.80902
<br />64
<br />43
<br />.6820
<br />.9325
<br />1.3673
<br />1.466
<br />1,072
<br />.73135
<br />47
<br />10
<br />.5901
<br />.7310
<br />1,2387
<br />1.695
<br />1.368
<br />,80730
<br />50
<br />1.0
<br />,0841
<br />.9380
<br />1.3711
<br />1.4621.066
<br />.72937
<br />• 50
<br />20.5925.73551.24131,6881.360,80558
<br />40
<br />20.8862.94351.37481,4571,060.72737
<br />40
<br />30
<br />.5948
<br />.7400
<br />1.2440
<br />1.6811,351
<br />,80886
<br />30
<br />30
<br />.6884
<br />.9490
<br />1.3790
<br />L.453
<br />1,054
<br />.72537
<br />30
<br />40.5972.74451,24661.6751.343.80212
<br />20
<br />40,6905.95451.38241.4481.048,72337
<br />20
<br />50
<br />.5995
<br />.7490
<br />1.24B4
<br />t.6681.335
<br />.80038
<br />1.0'
<br />50
<br />-6926
<br />.9601
<br />1-3883
<br />1.4441.042
<br />.72136
<br />10
<br />37
<br />.6018
<br />.7538
<br />1.2521
<br />1.662
<br />I X7
<br />.79864
<br />53
<br />44
<br />.6947
<br />, 9657
<br />1.3902
<br />1.440
<br />1.036
<br />.71984
<br />48
<br />10
<br />.6041
<br />.7581
<br />1.2549
<br />1.6551.319
<br />,79688
<br />50
<br />10
<br />,6967
<br />.9713
<br />1.3941
<br />t.435
<br />1.030
<br />.71732
<br />50
<br />20
<br />.6065
<br />.7627
<br />1.2577
<br />1.6491.311
<br />.79512
<br />40
<br />20
<br />.6988
<br />.9770
<br />1.3980
<br />1.431
<br />L.024
<br />.71529
<br />40
<br />30
<br />-6088
<br />,7673
<br />1.2605
<br />L6431,303
<br />.70335
<br />30
<br />30
<br />.7009
<br />,9827
<br />1.4020
<br />1,427
<br />1.018
<br />.71325
<br />30
<br />40
<br />.6111
<br />.7720
<br />1.2633
<br />1.636
<br />1,295
<br />.79158
<br />20
<br />40
<br />,7030
<br />-9884
<br />1.4061
<br />1,422
<br />1-012
<br />,71121
<br />20
<br />50
<br />.6134
<br />.7786
<br />1-2661
<br />1.630
<br />1,288-78980
<br />10
<br />50
<br />,7050
<br />.9942
<br />1.4101
<br />1.418
<br />1.006
<br />.709I6
<br />10
<br />38
<br />-6157
<br />.7813
<br />1.2600
<br />1.624
<br />1.280
<br />.78801
<br />52
<br />.7071
<br />1.
<br />1-414
<br />1,414
<br />1.
<br />.707I1
<br />45
<br />10
<br />.6180
<br />-78601.2714
<br />1.618
<br />1.272
<br />.78622
<br />50.
<br />20
<br />.6202
<br />.7907
<br />1,2748
<br />1.6121.265
<br />-76442
<br />40
<br />30
<br />,6225
<br />.7914
<br />1.3778
<br />1,606
<br />1.257
<br />.78261
<br />30
<br />40
<br />,6248
<br />.8002
<br />1.2809
<br />1.601
<br />1,250
<br />,78079
<br />20
<br />11
<br />50.6271
<br />.8030
<br />1.26361.595
<br />1.242
<br />,77897
<br />10
<br />i
<br />Colin, Cotg. Cosec. Sec. Tan. Sin. Angle i Cosln. Cog. Cosec. Sec. Tan. Sla, Angle
<br />TRIGONOMETRIC FORM[JLX
<br />i -
<br />a a
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin a , coo= b ,'tan = a ,cot = b ,sec = a , cosec = e
<br />c c b a b a
<br />(liven Required _ a
<br />a,b A,B,c tan A=h= cot B,c-Vlal+T2 a 1+¢z
<br />z
<br />'' �,.c•. A,B,b eigA=�=coaB,b=V'(o-I-a)(a-a)=a�1-ate
<br />a.
<br />�i A, a B, b, a B=90° -A, b = a cotA, a=
<br />B1II A.
<br />A,b-; B,a, c B=90°-A,a=btanA,e= b-
<br />C4B A.
<br />A, a B, a, b B -90'-A, a = c Bin A, b - e cos A,
<br />Solution of. Oblique Triangles
<br />Given. Required a Bin B
<br />! A, B, a b, c, C b = sin�A , Cr = 180°-(A + B), a -- sin A
<br />b sin A a sin C
<br />i Ay a, b B, c, C sin B= a .17- 180°-(A + 11), c = sin A
<br />(1, b, 'C A, B, C A+B=180°- C, tan I(A-B)= (a -b) tan. 1(A+B)
<br />ab
<br />a cin C +
<br />i e =
<br />sin A
<br />a+
<br />46 b, e A, B, C 8= 2+°,sin JA=-*, 8-- b(a--e ,
<br />einjB=Al ad ),C=180°--(A+B)
<br />a+b+c
<br />a, b, a AreL 8= Z
<br />A, b, a Areab e Bin A
<br />2
<br />A, B, C a Area area = W sin B sin C
<br />2 Bin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosineoftheverticalangle._Thus: slope distance=319.OL .
<br />eSt&��e .9959. Holizontal distance�51) 1W. Froe 918.4TableX Pa9959= S 8.09 fib° 10
<br />glow �flgls Horizontal distance also= Slope, distance minus slope
<br />e distance times (1-co;ine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 51 10+=.9959,1-.0959=.D041.
<br />310,4}(.0041=1.91. 319.4-1.31=318.09 ft.
<br />When the -rise is known, the horizontal distance is approxlmotely:-the slope dist-
<br />knee less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />jFape distance=3(116 it Horizontal distance=W26- 14_X 94 _302.6-0.32==28 fL
<br />V 2 X 8616
<br />MADE In V. CA,
<br />
|