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M17 LE5 Sem1 1011 - 5 points each 1 Jun observed from a...

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MATHEMATICS 17 Removal Exam 1st Sem / AY 2010-2011 I. Write TRUE if the given statement is always true. Otherwise, write FALSE. 1 pt each 1. If x is any real number, then x x 2 . 2. cot cos - 1 - 4 5 - 2 tan - 1 - 4 3 3. 3 - i 6 cis 165 ( 2 + i 2) 5 ( Write your final answer in rectangular form. ) II. Do as indicated. 1. 3 + 4 tan 3 2 x tan 3 2 x = cot 2 x + 3 csc 2 2 x , where x [0 , 2 π ) 2. sin - 1 cos x + π 4 = - π 3 3. cos - 1 x 2 + tan - 1 x = π 2 4. z 4 + 2 = 2 i 3 III. Graph one cycle of f ( x ) = 3 + 2 sin π 4 x + π 4 . Also, indicate its amplitude, period, and range. 5 points IV. Solve the following problems completely.
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Unformatted text preview: 5 points each 1. Jun observed from a rooftop that the angle of depression to a blue car in north is 60 ◦ while the angle of depression to a red car in south is 75 ◦ . If the red car and the blue car are 2 km apart from each other, how far is Jun from the two cars? 2. In the figure below, ± ABCD is a square and Δ ADE is a right triangle with AE = 6 and DE = 8. Find EF ? * END OF EXAM * TOTAL: 50 POINTS /ajdporlante 09.21.10/ 1...
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