C H A P T E R 5 Analytic Trigonometry

7. The hypotenuse of the larger right triangle is:
8.
F
(a)
0.6W sin 90
sin 12
F
(b) Let y1
0.6Wsin cos 90 cos sin 90
sin 12
0.6Wsin 0 cos 1
sin 12
0.6W cos
sin 12
0.6185 cos x
.
sin 12
0 90
0
(c) The force is maximum (533.88 pounds) when
The force is minimum (0 pounds) when 90.
550
0.
9. Seward:
Problem Solving for Chapter 5 527
New Orleans: D 12.2 1.9 cos
(a)
20
0 365
0
(b) The graphs intersect when t 91 and when t 274.
These values correspond to April 1 and October 1, the
spring equinox and the fall equinox.
(c) Seward has the greater variation in the number of daylight
hours. This is determined by the amplitudes, 6.4
and 1.9.
(d) Period:
10. when corresponds to 12:00 A.M.
(a) The high tides occur when cos Solving yields t 6.2 or t 18.6.
These t-values correspond to 6:12 A.M. and 6:36 P.M.
d 35 28 cos t 0
t 1.
6.2
6.2 t
D 12.2 6.4 cos
2
365.2 days
182.6
t 0.2
182.6
t 0.2
The low tide occurs when cos Solving yields t 0 and t 12.4 which corresponds to 12:00 A.M.
and 12:24 P.M.
t 1.
6.2
(b) The water depth is never 3.5 feet. At low tide the depth is d 35 28 7 feet.
(c)
θ
2
1
cos θ θ
sin
2
cos
2
70
1
sin θ
2(1 + cos θ )
sin
21 cos
sin 1 cos
21 cos 2
1 cos 1 cos 2
21 cos 21 cos
tan sin
2 1 cos
0 24
0
sin 2 1 cos 2 sin 2 1 2 cos cos 2
sin
21 cos
sin 1 cos
2 sin
1 cos
1 cos
1 cos
2
1 cos
2
2 2 cos
21 cos
182.6