17exerciseset4 - 2-tan θ 2 5. cos α + sin α cos α-sin...

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MATHEMATICS 17 Exercise Set 4 I. Evaluate the following. 1. cos 110 cos 160 - sin 110 sin 160 2. sin 5 x , given sin x = 5 - 1 4 3. cos π 7 cos 2 π 7 cos 4 π 7 4. cos 2 π 7 + cos 4 π 7 + cos 6 π 7 5. tan β 2 , if sin β + cos β = 7 2 and 0 < β < π 4 6. cos π 5 cos 2 π 5 7. cos π 5 + cos 3 π 5 8. cos 2 ± π 2 - θ ² - sin ³ 2 π 3 - θ ´ sin ± θ - π 3 ² 9. sin 13 π 20 cos 7 π 20 + cos 7 π 5 sin 11 π 10 10. 4 cos 4 ³ 3 π 8 ´ - 1 2 cos 2 ³ 3 π 8 ´ + 1 II. Do as indicated. 1. Given cos 4 α = 1 3 and tan β 2 = - 2, where P ( 4 α ) is not in Quadrant I and P ³ β 2 ´ is in Quadrant II. Find: (a) sin ³ 4 α + β 2 ´ (b) tan ³ 4 α - β 2 ´ (c) csc ± π 2 - 2 α ² 2. Sketch one cycle of the graph of the following. Give the period, amplitude, maximum and minimum, zeros, and phase displacement (if any). (a) y = 1 2 sin ± π 2 - 2 π x ² (b) y = 2 cos ± 3 x + π 2 ² - 1 III. Prove the following identities. 1. 1 = - cos 2 α h 1 + tan ± π 2 - α ² tan ( π - 2 α ) i 2. sec ± π 4 + ω ² sec ± π 4 + ω ² = 2 sec 2 ω 3. sin ( 2 α + β ) sin α - 2 cos ( α + β ) = sin α sin β 4. 2 ( csc 2 θ + cot 2 θ ) = cot θ
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Unformatted text preview: 2-tan θ 2 5. cos α + sin α cos α-sin α = tan ( 45 ◦ + α ) 6. cos α + sin α cos α-sin α = tan 2 α + sec 2 α 7. sin 2 ± π 8 + β ²-sin 2 ± π 8-β ² = sin 2 β √ 2 8. 2 cos 2 β-1 2 tan ± π 4-ω ² sin 2 ± π 4 + ω ² = 1 9. sin x + cos ( 2 y-x ) cos x-sin ( 2 y-x ) = 1 + sin 2 y cos 2 y 10. 2 ( sin 2 γ + 2 cos 2 γ-1 ) cos γ-sin γ-cos 3 γ + sin 3 γ = csc γ 11. sin φ-sin 3 φ + sin 5 φ cos φ-cos 3 φ + cos 5 φ = tan 3 φ 12. 2 ( sin 6 x + cos 6 x )-3 ± sin 4 x + cos 4 x ² + 1 = 13. 1-2 cos 2 ϕ sin ϕ cos ϕ = tan ϕ-cot ϕ 14. tan 2 A 2 = 2 sin A -sin 2 A 2 sin A + sin 2 A...
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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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