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14. The correct answer is (B). [+] Since angle x is measured in radians, set your calculator to the radian
mode. The value of x is the inverse cosine of 0.2586:
cos
–1
0.2586 = 1.3092
15. The correct answer is (B). [+] By definition, log
3
2 = x can be rewritten as 3
x
= 2. Solve for x by
taking the log of both sides of the equation:
Alternatively, you can use your calculator to test answer choices. Start with (C):
3
0.89
= 2.6585
Since that value is considerably more than 2, you should next test (B):
3
0.63
= 1.9979
So (B) must be the correct answer.
16. The correct answer is (D). [0] One way of attacking this problem is to examine the structure of the
two functions in light of the answer choices, but for most people that will probably be a matter of trial
and error.
Alternatively, you could substitute 3x – 6 into the answer choices until you find the formula that
generates the value x. But an even easier solution is to assign a value to x. Let x = 1. On that assump-
tion, f(1) = 3(1) – 6 = –3. Now, if you substitute –3 into the answer choices, the correct choice will
generate the value 1:
(A)
(B)
(C)
6 – 3(3) = –3 Wrong
(D)
(E)

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Mathematics Level IC/IIC Subject Tests
239
ARCO
■ SAT II Subject Tests
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17. The correct answer is (B). [0] Use an acute right triangle:
As for choices (A) and (C), sin 
and tan 
.
As for (D) and (E), sine and cosecant are reciprocal functions, so sin x · csc x = 1 and 
1
sin
x
= csc x.
18. The correct answer is (C). [+] Since the triangle is a right triangle, the shorter side and the longer
side can be used to find the area of the figure:
One way of finding the length of the longer side is:
Using the value 8 as the length of the longer side, we calculated the area of the triangle:

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Lesson 8
240
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ARCO
■ SAT II Subject Tests
This problem is assigned a “+” for calculator usage, because using the trig function of the calculator
seems the most natural approach. Given that the answer choices are fairly far apart, however, the prob-
lem can actually be solved without using a calculator. The 32
°–58–90° triangle of the problem is very
similar in shape to a 30
°–60°–90° triangle. And in a 30°–60°–90° triangle, the two sides are related in
the following way:
where s and l represent the shorter and longer sides, respectively. Therefore:
And:
Since s = 5:
And the area of a right triangle with sides of 5 and 8.5 would be:
The closest answer is (C).