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4
Logs and Trig
Logs and Trig
Source:
May 11, 2006
trigonometry
logarithms
Problem Statement
Given that
log
10
sin
x
+
log
10
cos
x
=
−
1
\log_{10} \sin x + \log_{10} \cos x = -1
lo
g
10
sin
x
+
lo
g
10
cos
x
=
−
1
and that
log
10
(
sin
x
+
cos
x
)
=
1
2
(
log
10
n
−
1
)
\log_{10} (\sin x + \cos x) = \textstyle \frac{1}{2} (\log_{10} n - 1)
lo
g
10
(
sin
x
+
cos
x
)
=
2
1
(
lo
g
10
n
−
1
)
, find
n
n
n
.
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