M17 LE4 Sem1 09-10 Solns - MATH 17 FOURTH LONG EXAM...

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Unformatted text preview: MATH 17 FOURTH LONG EXAM SOLUTIONS V7, W3, Y3 I. 1. f (- x ) = sin 2 (- x ) + cos (- x ) = (- sin x ) 2 + cos x = sin 2 x + cos x = f ( x ). Therefore, f is not odd but even, hence symmetric with respect to the y-axis. 2. 5 π < 16 < 11 π/ 2 . Thus, P (16) ∈ QIII and sin 16 is negative. 3. TRUE 4. TRUE 5. The range is (-∞ ,- 1] ∪ [1 , + ∞ ). II. 1. tan (- 555 ◦ ) = tan (- 360 ◦- 180 ◦- 15 ◦ ) =- tan 15 ◦ =- tan (45 ◦- 30 ◦ ) =- tan 45 ◦- tan 30 ◦ 1 + tan 45 ◦ tan 30 ◦ =- 1- √ 3 3 1 + 1 · √ 3 3 =- 3- √ 3 3 3 + √ 3 3 =- 3- √ 3 3 + √ 3 · 3- √ 3 3- √ 3 =- 12- 6 √ 3 6 = √ 3- 2 2. sin π 24 cos 5 π 24 = 1 2 sin π 24 + 5 π 24 + sin π 24- 5 π 24 = 1 2 sin π 4- sin π 6 = 1 2 √ 2 2- 1 2 = √ 2- 1 4 3. cot 73 π 13 = cot 6 π- 5 π 13 =- cot 5 π 13 =- tan π 2- 5 π 13 =- tan 3 π 26 4. cos 3 θ = cos (2 θ + θ ) = cos 2 θ cos θ- sin 2 θ sin 2 θ = (2cos 2 θ- 1)cos θ- (2sin θ cos θ )sin θ = 2cos 3 θ- cos θ- 2sin 2 θ cos θ...
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This note was uploaded on 08/05/2011 for the course MATH 17 taught by Professor Aaronjamesporlante during the Spring '11 term at University of the Philippines Diliman.

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M17 LE4 Sem1 09-10 Solns - MATH 17 FOURTH LONG EXAM...

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