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6 Solve, for 0°

6 Solve, for 0°

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q6 part i and j only

(Hint: In part d, write cos 30 as cos (20 + 0).) 5 Use double-angle formulae to solve, for 0 < x < 2n: a sin 2x = sin x b sin 2x + V3 cos x = 0 %3D C 3 sin x + cos 2x = 2 d cos 2x + 3 cos x + 2 = 0 %D %3D e tan 2x + tan x = f sin 2x = tan x 6 Solve, for 0° < 0 < 360°, giving solutions correct to the nearest minute where necessary: a 2 sin 20 + cos 0 = 0 b 2 cos? 0 + cos 20 = 0 d 8 sin? 0 cos?0 = 1 %3D C 2 cos 20 + 4 cos 0 = 1 %3D %3D cos 20 = 3 cos² 0 – 2 sin² 0 h tan 0 = 3 tan ,0 e 3 cos 20 + sin 0 = 1 f %3D g 10 cos 0 + 13 cos 0 = 5 %3D %3D I cos 20 = sin 0 2. į cos 20 + 3 = 3 sin 20 %3D Hint: Use sin? 0 = } - ¿ cos 20.) (Hint: Write 3 as 3 cos? 0 + 3 sin? 0.) %D 7 Consider the equation tan ( + 0) = 3 tan (: - 0). a Show that tan? 0 – 4 tan 0 + 1 = 0. %3D 4 4 %3D b Hence use the quadratic formula to solve the equation for 0 < 0 < T. 8 Given the equation 2 cos x – 1 = 2 cos 2x: %3D a Show that cos x = }(1 + V5 ) }(1 - v5 ). or cos x = b Hence solve the equation for 0 < x < 2n. 9 a Show that sin (a + B) sin (a - B) = sin²a – sin² ß. b Hence solve the equation sin? 30 – sin?0 = sin 20, for 0 < 0 < T. %3D 10 2 Show that ain
Transcribed Image Text:(Hint: In part d, write cos 30 as cos (20 + 0).) 5 Use double-angle formulae to solve, for 0 < x < 2n: a sin 2x = sin x b sin 2x + V3 cos x = 0 %3D C 3 sin x + cos 2x = 2 d cos 2x + 3 cos x + 2 = 0 %D %3D e tan 2x + tan x = f sin 2x = tan x 6 Solve, for 0° < 0 < 360°, giving solutions correct to the nearest minute where necessary: a 2 sin 20 + cos 0 = 0 b 2 cos? 0 + cos 20 = 0 d 8 sin? 0 cos?0 = 1 %3D C 2 cos 20 + 4 cos 0 = 1 %3D %3D cos 20 = 3 cos² 0 – 2 sin² 0 h tan 0 = 3 tan ,0 e 3 cos 20 + sin 0 = 1 f %3D g 10 cos 0 + 13 cos 0 = 5 %3D %3D I cos 20 = sin 0 2. į cos 20 + 3 = 3 sin 20 %3D Hint: Use sin? 0 = } - ¿ cos 20.) (Hint: Write 3 as 3 cos? 0 + 3 sin? 0.) %D 7 Consider the equation tan ( + 0) = 3 tan (: - 0). a Show that tan? 0 – 4 tan 0 + 1 = 0. %3D 4 4 %3D b Hence use the quadratic formula to solve the equation for 0 < 0 < T. 8 Given the equation 2 cos x – 1 = 2 cos 2x: %3D a Show that cos x = }(1 + V5 ) }(1 - v5 ). or cos x = b Hence solve the equation for 0 < x < 2n. 9 a Show that sin (a + B) sin (a - B) = sin²a – sin² ß. b Hence solve the equation sin? 30 – sin?0 = sin 20, for 0 < 0 < T. %3D 10 2 Show that ain
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