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MAA AMC
AMC 12/AHSME
1980 AMC 12/AHSME
18
Trig Log
Trig Log
Source:
December 31, 2005
trigonometry
logarithms
Problem Statement
If
b
>
1
b>1
b
>
1
,
sin
x
>
0
\sin x>0
sin
x
>
0
,
cos
x
>
0
\cos x>0
cos
x
>
0
, and
log
b
sin
x
=
a
\log_b \sin x = a
lo
g
b
sin
x
=
a
, then
log
b
cos
x
\log_b \cos x
lo
g
b
cos
x
equals
(A)
2
log
b
(
1
−
b
a
/
2
)
(B)
1
−
a
2
(C)
b
a
2
(D)
1
2
log
b
(
1
−
b
2
a
)
(E) none of these
\text{(A)} \ 2\log_b(1-b^{a/2}) ~~\text{(B)} \ \sqrt{1-a^2} ~~\text{(C)} \ b^{a^2} ~~\text{(D)} \ \frac 12 \log_b(1-b^{2a}) ~~\text{(E)} \ \text{none of these}
(A)
2
lo
g
b
(
1
−
b
a
/2
)
(B)
1
−
a
2
(C)
b
a
2
(D)
2
1
lo
g
b
(
1
−
b
2
a
)
(E)
none of these
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