topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x...

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Subject – Math(Higher Level) Topic - Circular trigonometry Year - Nov 2011 – Nov 2017 Question -1 Question-2

Transcript of topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x...

Page 1: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Subject–Math(HigherLevel)Topic-Circulartrigonometry

Year-Nov2011–Nov2017Question-1

Question-2

Page 2: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question3

Page 3: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question-4

Question-5

Page 4: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question–6

Question-7

Page 5: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question-8

Question9

Page 6: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question10

Question11

Page 7: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question12

Question13

Page 8: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question14

Question15

Question16

Page 9: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question17

Page 10: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question18

Page 11: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question19

Page 12: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

Question20

Page 13: topical - Math -HL-Answer-2011-2017- Circular trigonometry filesin — cos 3xsin x sm x cosx sin (3x — x) sin 2x OR sin 2x cosx + cos 2x sin x smx 2 sinxcos2 x +2cos2 xsinx sinx

1 Differentiation trigonometric functions.notebook€¦ · — cos cos 2 x 4 sec4 x tan x 4 tan3 x sec2 x tan2 -x sec2 -x sec2 x tan2 tan2 x tan 21 + 2x sec2 2x sin + sin2 x) cos4

1 Differentiation trigonometric functions.notebook€¦ · — cos cos 2 x 4 sec4 x tan x 4 tan3 x sec2 x tan2 -x sec2 -x sec2 x tan2 tan2 x tan 21 + 2x sec2 2x sin + sin2 x) cos4

NATIONAL SENIOR CERTIFICATE EXAMINATION · PDF fileArea DGEF = DE x EF = x tan 60 ⁰ (3 – 2x) = x. 3.(3 – 2x) = 3.x (3 – 2x) EF = 3 – 2x x tan 60⁰ (3 – 2x) (2) 8.3 A(x)

NATIONAL SENIOR CERTIFICATE EXAMINATION · PDF fileArea DGEF = DE x EF = x tan 60 ⁰ (3 – 2x) = x. 3.(3 – 2x) = 3.x (3 – 2x) EF = 3 – 2x x tan 60⁰ (3 – 2x) (2) 8.3 A(x)

Scanned with CamScanner · 2019. 12. 1. · cos4 x — sin4 x = cos 2x = I + sin2x (sin x + cos x)2 I + cos I()y = 2 cos2 5y 59. 6 sin — cos — 61. sin 59 cos 39 63. 5 cos(—5ß)

Scanned with CamScanner · 2019. 12. 1. · cos4 x — sin4 x = cos 2x = I + sin2x (sin x + cos x)2 I + cos I()y = 2 cos2 5y 59. 6 sin — cos — 61. sin 59 cos 39 63. 5 cos(—5ß)

eprints.usm.myeprints.usm.my/27936/1/EUM_102_-_MATEMATIK_KEJURUTERAAN_II_APRIL_1… · [BUM 102] kebezaan yang baihit: cos 2x = l, 7 y = COS X X e —X sin x 8y + 16 cos 2x , (40%)

eprints.usm.myeprints.usm.my/27936/1/EUM_102_-_MATEMATIK_KEJURUTERAAN_II_APRIL_1… · [BUM 102] kebezaan yang baihit: cos 2x = l, 7 y = COS X X e —X sin x 8y + 16 cos 2x , (40%)

If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x.

If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x.

Answers - Nulake · 36 99 36 13 Page 38 186. dy dx = 2x cos x – x2 sin x 187. dy dx = 3 tan 3x + (9x – 6) sec2 3x 188. g’(x) = dy dx = 2x cot(5x – 1)

Answers - Nulake · 36 99 36 13 Page 38 186. dy dx = 2x cos x – x2 sin x 187. dy dx = 3 tan 3x + (9x – 6) sec2 3x 188. g’(x) = dy dx = 2x cot(5x – 1)

ANALYTIC TRIG!!!!!!!. Trig Identities sin^2x + cos^2x = 1 tan^2x + 1 = sec^2x 1 + cot^2x = csc^2x sin(-x) = -sinx cos(-x) = cosx tan(-x) = -tanx.

ANALYTIC TRIG!!!!!!!. Trig Identities sin^2x + cos^2x = 1 tan^2x + 1 = sec^2x 1 + cot^2x = csc^2x sin(-x) = -sinx cos(-x) = cosx tan(-x) = -tanx.

x·,n I - Kirkland Mastery Math 1 Ch 22.pdf22C 1) (3X+4)(X+1) X+11 1=1 ~ 2) (2X + 3)(X + 2) 9) 10) (2X + 1)(2X + 3) 2X + 1 x 2X + 3 6X + 3 4X2 + 2X 3X + 4 4X2 + 8X + 3 x + 2 11) 82+6-5

x·,n I - Kirkland Mastery Math 1 Ch 22.pdf22C 1) (3X+4)(X+1) X+11 1=1 ~ 2) (2X + 3)(X + 2) 9) 10) (2X + 1)(2X + 3) 2X + 1 x 2X + 3 6X + 3 4X2 + 2X 3X + 4 4X2 + 8X + 3 x + 2 11) 82+6-5

y!=!$4x!–!7! !! ! 2x!$!3y!=!6! !!!!!y!=!$4x!–!7! !! ! 2x!$!3y!=!6! !!!!!y!=!3x 2!–!4x!+!7!!!!!y!=!sin!(x!–!3)!+!5!!! ! Function(Notation !!!!! ! ! ! ! ! !! f(1)!=! ! ! ! !

y!=!$4x!–!7! !! ! 2x!$!3y!=!6! !!!!!y!=!$4x!–!7! !! ! 2x!$!3y!=!6! !!!!!y!=!3x 2!–!4x!+!7!!!!!y!=!sin!(x!–!3)!+!5!!! ! Function(Notation !!!!! ! ! ! ! ! !! f(1)!=! ! ! ! !

EXERCICESEXERCICES Algèbre Algèbre :::: …...2 Révision algèbre deuxième secondaire 1. x + x = 2. x + 2x = 3. y + 3y = 4. x + y + x = 5. x + y = 6. x3 + 2x 3 – 3x 2 = 7. 2x

EXERCICESEXERCICES Algèbre Algèbre :::: …...2 Révision algèbre deuxième secondaire 1. x + x = 2. x + 2x = 3. y + 3y = 4. x + y + x = 5. x + y = 6. x3 + 2x 3 – 3x 2 = 7. 2x

Central Bucks School District / Homepage · 2016. 12. 21. · c) tan 2x= : 3Fi X b) cos 2x= a) sin 2x= Verify by finding 0 (use cos) sin2x — 2sinxcosx Examples: 1) If sin x= a)

Central Bucks School District / Homepage · 2016. 12. 21. · c) tan 2x= : 3Fi X b) cos 2x= a) sin 2x= Verify by finding 0 (use cos) sin2x — 2sinxcosx Examples: 1) If sin x= a)

dstharyana.orgdstharyana.org/html/whtsnew/2012/Nov Science Quiz/Sample... · Web view(2x cos y + y² cos x) dx + (2y sin x - x² sin y) dy = 0 is (a) x² cos y + y² sin x = c (b)

dstharyana.orgdstharyana.org/html/whtsnew/2012/Nov Science Quiz/Sample... · Web view(2x cos y + y² cos x) dx + (2y sin x - x² sin y) dy = 0 is (a) x² cos y + y² sin x = c (b)

hoc360.net...+ COS 2À 2 cos 2 — cos 2x cos 2x f(x)dx ex + sin 2x + C — ex + tan X +

hoc360.net...+ COS 2À 2 cos 2 — cos 2x cos 2x f(x)dx ex + sin 2x + C — ex + tan X +

 · Exercise 5.3 2x + 3y = sin x Differentiating both sides with respect to x, we get — sin x dx dx dx dy cosx — 2 dx 2x + = sin y dy dx cos x Question 2: 2x + = sin y Answer

 · Exercise 5.3 2x + 3y = sin x Differentiating both sides with respect to x, we get — sin x dx dx dx dy cosx — 2 dx 2x + = sin y dy dx cos x Question 2: 2x + = sin y Answer

Math 1431 - Section 16679bekki/1431/notes/1431day04.pdf · 1 lim x!0 sin(5x) 5x = 2 lim x!0 sin(5x) x = 3 lim x!0 sin(5x) 2x = Bekki George (UH) Math 1431 08/29/19 15/50. Section

Math 1431 - Section 16679bekki/1431/notes/1431day04.pdf · 1 lim x!0 sin(5x) 5x = 2 lim x!0 sin(5x) x = 3 lim x!0 sin(5x) 2x = Bekki George (UH) Math 1431 08/29/19 15/50. Section

 · 2 cot 4x 2 tan x + sec x x2 cos 2x 1 + sin x cos x tan 4 3x cos 2x f'(x) = (x + cos x)2 — + COS — (it) — 2 — + COS 2. 8. 11. 14. 20. 1 — sin — cos 3x y — —cosec

 · 2 cot 4x 2 tan x + sec x x2 cos 2x 1 + sin x cos x tan 4 3x cos 2x f'(x) = (x + cos x)2 — + COS — (it) — 2 — + COS 2. 8. 11. 14. 20. 1 — sin — cos 3x y — —cosec

sin40 cos10 cos40 sin10 q q q q As cos( x y sin y cos xcos ... · As cos(x- y) = sin y cos xcos y + sin xsin y = sin y (1) D r aw a ight- ngled t , ... tan 2x = 2 tan x 1- tan2 x

sin40 cos10 cos40 sin10 q q q q As cos( x y sin y cos xcos ... · As cos(x- y) = sin y cos xcos y + sin xsin y = sin y (1) D r aw a ight- ngled t , ... tan 2x = 2 tan x 1- tan2 x

BRG/BORG Dornbirn Schoren - BRG/BORG Dornbirn Schorenteachers.brg-schoren.ac.at/sere/mathe/2014_2015_8b/docs/... · Web viewcos 2x dx L: 1 2 ∙sin 2x +c d) sin x ∙ cos 2 x dx L:

BRG/BORG Dornbirn Schoren - BRG/BORG Dornbirn Schorenteachers.brg-schoren.ac.at/sere/mathe/2014_2015_8b/docs/... · Web viewcos 2x dx L: 1 2 ∙sin 2x +c d) sin x ∙ cos 2 x dx L:

2x − 3 = 9 (a + b) 2 = a 2 + 2ab + b 2 x + 5 = 6 (x − 1) 2 = x 2 + 2x + 1 2x = 12 + x.

2x − 3 = 9 (a + b) 2 = a 2 + 2ab + b 2 x + 5 = 6 (x − 1) 2 = x 2 + 2x + 1 2x = 12 + x.

...sin2A + sin2B + sin2C The value of is equal to sinA + sinB + sinc (A) sin—sin—sin— (B) 2sin — sin — sin — (D) 8sin—sin—sin— If x + y + z xyz prove that 2x 2y 2z

...sin2A + sin2B + sin2C The value of is equal to sinA + sinB + sinc (A) sin—sin—sin— (B) 2sin — sin — sin — (D) 8sin—sin—sin— If x + y + z xyz prove that 2x 2y 2z