An arco book arco is a registered trademark of Thomson Learning, Inc., and is used herein under license by Peterson’s. About The Thomson Corporation and Peterson’s

Lesson 8
242
w w w . p e t e r s o n s . c o m / a r c o
ARCO
■ SAT II Subject Tests
26. The correct answer is (C). [0] By definition, the logarithm of a number, to a given base, is the ex-
ponent that is used with the base to obtain that number:
b
e
= n 
↔ e = log
b
n
Here the base, b, is 3, and the number, n, is 
. So all you need to do is rewrite the statement in its
equivalent exponential form:
3 to what power equals
Since the fractional exponent 1/2 indicates “square root,” the statement should read:
3 to the 
1
2
power equals
27. The correct answer is (A). [+] The best approach to this problem is to use your calculator to find
the value of f
–1
(2.5):
So f
–1
(2.5) = 
1
2 3884
.
= 0.4186. And (A) is the best answer.
28. The correct answer is (E). [0] The following table summarizes the behavior of the trigonometric
functions in the first quadrant:
y = sin x
increases from 0 to 1
y = cos x
decreases from 1 to 0
y = tan x
increases from 0 to 
∞
y = cot x
decreases from 
∞ to 0
y = sec x
increases from 1 to 
∞
y = csc x
decreases from 
∞ to 1
You could also solve this problem by sketching a graph of the functions.
29. The correct answer is (D). [0] Arcsin s indicates the angle for which the sine is s, and Arcsin d
indicates the angle for which the sine is d. Since Arcsin s is twice Arcsin d, angle x must be twice the
unmarked angle. Since those two angles are complementary, x must be 60.