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University of the Philippines, ManilaCollege of Arts and Sciences

Department of Physical Sciences and MathematicsMATH 17: College Algebra and Trigonometry

First Departmental ExamOctober 14, 2011

I - TRUE OR FALSE: Write TRUE if the given statement is accurate; otherwise, write FALSE . (2 pts each)

1. A course of 195 is similar to a bearing of 165 North of West.

2. Arcsin sin34

=34

.

3. tan2 Arccot

725

=725

.

4. sin(Arctan( x )) = x 1 + x 2 .

5. In ABC , if A , and sides a and b are known, and a > b sin A , then there are two possible triangles that maybe formed.

6. If the angle of elevation from A to B is , and the angle of elevation from B to C is , then the angle of elevationfrom A to C is .

7. In right triangle ABC , with right angle at C , sin A = cos B .

8. In ABC , if C is obtuse, then a 2 + b2 < c 2 .

9. The point with polar coordinates 4,12

has rectangular coordinates 2 + 6

2, 2

62

10. (cos i sin )n = cos( n ) i sin(n ).

II- MULTIPLE CHOICE: Choose the letter of the best answer. If an appropriate answer is not among thechoices, write E .

1. After Typhoon Ondoy hit Manila, a tree along Padre Faura broke without breaking off from its base, such thatthe top of the tree hit the ground 3 feet from its base, and forming an angle of 60 with the ground. How tallwas the tree?A. 3 ftB. 3 3 ftC. 6 + 3 ftD. 6 + 3 3 ft

2. A triangle has sides of lengths 23 cm, 34 cm, and 42 cm. Find the measure of the smallest angle.A. 23

B. 33

C. 53

D. 69

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3. Which of the following given cannot form a triangle?A. = 69 , = 81 , c = 10B. = 96 , b = 29, c = 28

C. = 57

, a = 18, b = 20D. = 36 , a = 6 .5, b = 12

4. Which of the following given results in two possible triangles?A. = 69 , = 81 , c = 10B. = 96 , b = 29, c = 28C. = 57 , a = 18, b = 20D. = 36 , a = 6 .5, b = 12

5. Which of the following is the solution for x in cot (Arctan( x ) + Arcsin(1))?A. -3B. 0C. 1D. 3

III- PROBLEM SOLVING: Show all necessary solutions for each of the following problems. :

1. From the top of a building 60 ft high, the angle of elevation to the top of a vertical pole is 15 . From the footof the building, the angle of elevation to the top of the pole is 75 . How high is the pole? (You may leave your

answers as a decimal rounded to three decimal places)2. Two automobiles leave a city at the same time and travel along straight highways that differ in direction by 84 .

If their speeds are 60 mi/hr and 45 mi/hr, respectively, approximately how far apart are the cars at the end of 1 hour 20 minutes? (You may leave your answers as a decimal rounded to three decimal places)

3. Evaluate: cos Arcsin35

+ Arctan 724

4. Evaluate: (2 2 3i)8

5. Find the six 6th roots of 64 in rectangular form.

Numbers are funny. They can measure you, time you, analyze you all they want. But in the end, all that matters is how you play the game... You ever hear the expression You cant measure heart? The truth is you cant measure any of it. Heart, want, need... You cant measure a dream.

-Nathan Scott, One Tree Hill

-END OF EXAM-()

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