Chapter 7: Small Angles & Approximation
Example 2
If
q
is small enough to neglect
q
3
term and above, show that
4 sin (
p
/4
-
2
q
)
»
2
Ö
2 (1
-
2
q
-
2
q
2
).
Solution
4 sin (
p
/4
-
2
q
)
=
4(sin
p
/4 cos 2
q
-
cos
p
/4 sin 2
q
)
=
4
¾
(cos 2
q
-
sin 2
q
)
Ö
2
»
4
¾
[1
-
½(2
q
)
2
-
2
q
]
Ö
2
=
4
Ö
2
¾.¾
(1
-
2
q
-
2
q
2
)
Ö
2
Ö
2
=
2
Ö
2 (1
-
2
q
-
2
q
2
)
Index
