Mathematics 17
Fifth Long Exam
GENERAL DIRECTION:
Write the exam code of the test paper at the upper right corner of your
bluebook (front). Write your student number below the code. Show all necessary solutions and box the final
answers. Refrain from using calculators. Leave all radical expressions (
√
2,

√
5, etc.) in its form, unless if
it can be simplified. Cheating is punishable by deduction.
I. Solve for the value of
x
. Check your final answers.
[4 points each]
1. 3 cos
x

sin 2
x
= 0 where 0
≤
x <
2
π
2. sec
5
x
= 4 sec
x
where 0
≤
x <
2
π
3.
x
= cos[Arctan
15
17

Arcsin
8
17
]
4. Arccot
x
+
π
4
= Arccos[cos(

π
3
)]

Arcsin
√
2
2
5. Arccos
1
x
+ Arctan
1
2
x
=
π
2
II. Do as indicated.
1. Let
y
be the remainder when the RIGHTMOST DIGIT of your student number is divided by 4. Convert
the assigned item to its rectangular form and find its 2 square roots. All trigonometric expressions should
be simplified.
[5 points]
remainder 0: cis
π
4
remainder 2: cis
5
π
4
remainder 1: cis
3
π
4
remainder 3: cis
7
π
4
2. Simplify.
[4 points]
i
102
(3
√
3

3
i
)
5
(
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 Summer '11
 AaronJamesPorlante
 Math, Algebra, Trigonometry, Cos, Inverse trigonometric functions, tan α

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