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Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 38E
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2:27 Discussion Details ( Back Calculus 1 Find f' (E), f" (), s" (), given f (æ) = sin æ cos 3a f' (x) = -3 sin x sin 3x + cos 3x cos x f' (æ) = -2 sin x sin 3x – 1 sin x sin 3x + cos 3x cos x f' (x) = (cos 3x cos x – sin 3x sin x) – 2 sin x sin 3x from the formula of sum and difference of two angles identities: cos(x + y) = cos x cos y sin x sin y . cos (3x + x) = cos 3x cos z - sin 3x sin x + cos 4x = cos 3x cos z - sin 3x sin z f' (x) : = cos 4x – 2 sin x sin 3x Substitute 3 * (;) 4(품) - 2 sin(#) sin 3 () = cos 4 But T = 180 () 180 180 180 = cos 4 3 - 2 sin sin 3 3 4 (50) → - why? because 4 (60) = 240 and cos 240° = and V3 V3 * why? because sin 60° 180 sin 3 2 1 Previous Next 203 Dashboard Calendar To Do Notifications Inbox ..
Transcribed Image Text:2:27 Discussion Details ( Back Calculus 1 Find f' (E), f" (), s" (), given f (æ) = sin æ cos 3a f' (x) = -3 sin x sin 3x + cos 3x cos x f' (æ) = -2 sin x sin 3x – 1 sin x sin 3x + cos 3x cos x f' (x) = (cos 3x cos x – sin 3x sin x) – 2 sin x sin 3x from the formula of sum and difference of two angles identities: cos(x + y) = cos x cos y sin x sin y . cos (3x + x) = cos 3x cos z - sin 3x sin x + cos 4x = cos 3x cos z - sin 3x sin z f' (x) : = cos 4x – 2 sin x sin 3x Substitute 3 * (;) 4(품) - 2 sin(#) sin 3 () = cos 4 But T = 180 () 180 180 180 = cos 4 3 - 2 sin sin 3 3 4 (50) → - why? because 4 (60) = 240 and cos 240° = and V3 V3 * why? because sin 60° 180 sin 3 2 1 Previous Next 203 Dashboard Calendar To Do Notifications Inbox ..
2:27 Discussion Details < Вack Calculus 1 180 180 180 = cos 4 ( 00) – 2 sin sin 3 3 3 () 180 cos 4 - why? because 4 (60) = 240 and cos 240° = and sin (10) W why? because sin 60° 3 2 see figure below 2 2 2 -1 V3 (0, 1) (1 v3 ) (cos 0, sin 0) 2 2 /2 /2 2'2 V3 1 2 '2 2 '2 (-13 1) 2 2. 150° =5n/6 300-n6 (-1, 0) 180° =R (1, 0) 330° =11n/6 0°=On=2n V3 -1 210° =7n/6 V3 -1 2 '2 2 2 (-12 225으%35m/4- V2 V2 - V2 2'2 2 2 -1 -3 V3 2 ) (0, -1) (2' 2 (Figure is from: shorturl.at/cmqvA) r (금) 3%3 -2 () (0) r (중) 33 2 Now try to find f" (x) and f" (x). solution on Solve Problems for Differentiation of you can upload your Trionomatric Eunotions ( Previous Next 203 Dashboard Calendar To Do Notifications Inbox ... 120으%=2짜/3 135º =3n/4 3150 =7n/4 300º =5x/3 270º =3n/2
Transcribed Image Text:2:27 Discussion Details < Вack Calculus 1 180 180 180 = cos 4 ( 00) – 2 sin sin 3 3 3 () 180 cos 4 - why? because 4 (60) = 240 and cos 240° = and sin (10) W why? because sin 60° 3 2 see figure below 2 2 2 -1 V3 (0, 1) (1 v3 ) (cos 0, sin 0) 2 2 /2 /2 2'2 V3 1 2 '2 2 '2 (-13 1) 2 2. 150° =5n/6 300-n6 (-1, 0) 180° =R (1, 0) 330° =11n/6 0°=On=2n V3 -1 210° =7n/6 V3 -1 2 '2 2 2 (-12 225으%35m/4- V2 V2 - V2 2'2 2 2 -1 -3 V3 2 ) (0, -1) (2' 2 (Figure is from: shorturl.at/cmqvA) r (금) 3%3 -2 () (0) r (중) 33 2 Now try to find f" (x) and f" (x). solution on Solve Problems for Differentiation of you can upload your Trionomatric Eunotions ( Previous Next 203 Dashboard Calendar To Do Notifications Inbox ... 120으%=2짜/3 135º =3n/4 3150 =7n/4 300º =5x/3 270º =3n/2
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