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

152 Chapter 3 The trigonometric functions
16 Avoltage, v(t),varieswith time,t,according to
v(t) = 240sin(100πt +30) t 0
Find the firsttime that v(t)has avalue of
(a) 240 (b) 0
(c) −240 (d) 100
17 Simplify asfar aspossible
(a) cos100 ◦ +cos80 ◦
(b) cos100 ◦ −cos80 ◦
sin50 ◦ +sin40 ◦
(c)
cos5 ◦
(d) sin80◦ −sin60 ◦
2sin10 ◦
Solutions
1 (a)
π
4
(b)
2π
5
(d) 5.2360 (e) 7.6794
(c) 1.7453
2 (a) 60 ◦ (b) 540 ◦ (c) 135 ◦
(d) 114.6 ◦ (e) 207.4 ◦
3 (a) 1st (b) 4th (c) 3rd
(d) 3rd (e) 2nd
4 (a) 1 (b) cosx (c) cosecA
(d) tanA (e) 1
5 (a) 2 (b) tan2A (c) tanx
(d) sin2t (e) tan 2 A
6 (a) sin2x (b) 2 (c) cot θ
( )
t
(d) sin4A (e) 2sin
2
7 (a) 2,3, 2π 3 , 3
2π ,0,0
(b) 4,6, π 3 , 3 π ,0,0
(c) 0.7,2, π, 1 π ,3, 3 2
(d) 0.1, π,2, 1 2 ,0,0
(e) 1,50π,0.04,25,20, 2
5π
(f) 6,100π,0.02,50, −30, − 3
10π
1
(g)
2 , 1 2 ,4π, 1
4π ,0,0
(h) 0.25,2π,1,1,1, 1
2π
√
8 (a) 61sin(5t +0.6947)
√
(b) 0.05sin(t +5.1760)
√
(c) 85sin(3t +0.7086)
(d)
(e)
9 (a)
( )
√ t 97sin
2 +1.9890
√
234sin(2t +1.3734)
√
58sin(4t −5.1173)
(b) √ 34sin(2t −3.6820)
√
(c) 65sin(6t −1.0517)
5
(d) sin(t −5.6397)
6
(e) 1.4577sin(0.5t −1.0304)
√
10 (a) 356cos(3t +5.7246)
(b) √ 45cos(2t +2.0344)
√
(c) 5cos(t +3.6052)
(d) √ 2.05cos(4t +5.1448)
√
(e) 26cos(7t +1.3734)
11 (a) 6.8007cos(3t −0.3450)
12 (a)
(b) √ 5cos(2t −3.6052)
√
(c) 85cos(9t −1.3521)
(d) √ 41cos(4t −0.6747)
( )
√ t
(e) 40cos
2 −3.4633
√
2sin(t +1.7854)
(b) 1.4451sin(2t +5.0987)
(c) 2.9725sin(3t +0.7628)
(d) 1.0806sin(t +2)
(e) 2.4654sin(2t +4.8828)
√ √
13 (a) 13sin(ωt +0.5880), amplitude = 13,phase
angle = 0.5880
(b) 0.765sin(ωt +1.1781),amplitude = 0.765,
phaseangle = 1.1781
(c) 5.596sin(ωt +2.10),amplitude = 5.596, phase
angle = 2.10