082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

150 Chapter 3 The trigonometric functions
3 (a) 0.7041, 3.8457 (b) 0.9927, 4.1343
(c) 0.8961, 4.0376 (d) 2.4408, 5.5824
(e) 2.0225, 5.1641 (f) 2.1370, 5.2786
4 (a) 0.3438,1.2270, 3.4854, 4.3686
(b) 1.1320,2.0096, 3.2264, 4.1040, 5.3208, 6.1984
(c) 0.8779,5.4053
(d) 1.4071,2.3053, 4.5487, 5.4469
(e) 1.5846,2.9862, 4.7262, 6.1278
(f) nosolutions
5 (a) 0.5668,2.5748, 3.7084, 5.7164
(b) nosolutions
(c) 1.3504
(d) 1.0250,1.6166, 4.1665, 4.7582
(e) 1.2669, 2.7331
(f) 0.9971, 1.6396, 2.9971, 3.6396, 4.9971, 5.6396
6 (a) 0.4950, 2.0658, 3.6366, 5.2073
(b) no solutions
(c) 0.9388, 1.9860, 3.0332, 4.0804, 5.1276, 6.1748
(d) 2.0633, 4.1577, 6.2521
(e) 0.6781, 5.3905
(f) 0.3939, 1.0222, 1.6505, 2.2788, 2.9071, 3.5355,
4.1638, 4.7921, 5.4204, 6.0487
7 (a) 1.2038 ×10 −2
(b) 9.3427 ×10 −3
(c) 7.2771 ×10 −3
TechnicalComputingExercises3.8
1 Ploty = sint for0 t 2π andy = 0.3500 using
the same axes. Useyour graphs to find approximate
solutionsto
sint =0.3500
0t 2π
2 Ploty = cost for0 t 2π andy = −0.5500using
the same axes. Useyour graphs to find approximate
solutionsto
cost+0.5500=0
0t2π
3 Ploty=sin(2t+1)andy=2sintfor0t 2π.
Useyourgraphs to stateapproximate solutionsto
sin(2t+1)=2sint
0t 2π
4 Ploty=2sin3tandy=3cos2tfor0t 2π.
Hence state approximate solutionsof
2sin3t =3cos2t
0t 2π
REVIEWEXERCISES3
1 Expressthe followingangles in radians:
(a) 45 ◦ (b) 72 ◦ (c) 100 ◦ (d) 300 ◦
(e) 440 ◦
2 Thefollowing angles are in radians. Expressthemin
degrees.
π 3π
(a) (b) 3π (c) (d)2 (e) 3.62
3 4
3 Statethe quadrant in whichthe angle α liesgiven
(a) sinα>0andtanα>0
(b) cosα>0andsinα<0
(c) tanα>0andcosα<0
(d) sinα<0andcosα<0
(e) tanα<0andcosα<0
4 Simplify the followingexpressions:
(a) sint cosect
sinx
(b)
tanx
cotA
(c)
cosA
secA
(d)
cosecA
(e) cotxtanx
5 Simplify the following expressions:
(a) cos 2 A +1+sin 2 A
2sinAcosA
(b)
cos 2 A −sin 2 A
√
(c) sec 2 x−1
(d) sintcost +
(e)
1
cosec 2 A −1
1
sect cosect