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M17 LE4 Sem1 09-10 Solns

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

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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 = 2cos 3 θ - cos θ - 2(1 - cos 2 θ )cos θ = 2cos 3 θ - cos θ - 2cos θ + 2cos 3 θ = 4cos 3 θ - 3cos θ = 4 m 3 - 3 m III. 1. We are given cos 2 A = - 1 4 and π 2 < 2 A < π which implies that π 4 < A < π 2 .

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

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