C H A P T E R 5 Analytic Trigonometry

522 Chapter 5 Analytic Trigonometry
97.
101.
sin 4 sin 2 2 cos
r 1
32 v 0 2 sin 2
range 100 feet
v 0 80 feet per second
r 1
32 802 sin 2 100
sin 2 0.5
2 30
15 or
12
102. Volume V of the trough will be the area A of the isosceles triangle times the length l of the trough.
(a)
(b)
V A l
A 1
2 bh
cos h
2 0.5
sin
2
b
2
0.5
A 0.5 sin
0.5 cos
2 2
V 0.254 sin
2
sin
2
V sin
2
2 cos 3 sin
0.52 sin
cos
2 2
0.25 sin
2
4 2
99. cosx 6 cosx 2 sin x sin 6 6
⇒ h 0.5 cos
2
b
⇒ 0.5 sin
2 2
cos square meters
2
cos cubic meters
2
cos cubic meters
2
1
cos 2 sin cos
2 2 2 2
Volume is maximum when
2 .
2
sin 4 2
2 98.
1
sin cubic meters
2
0.5 m
cos 3 cos 2 2 cos
4 m
b
h
0.5 m
Not drawn to scale
3 2
2
2 cos 5
cos
2 2
100. 2 cos x sin
sinx sin
4
x 2 cosx
4
x 4 x
sin 4
2
x 4
2
4
4
3 2
cos
2