Add Math Trigonometric Function

Form 5 Paper 1 and 2 Chapter 5

Paper 2, Section A [7 8 Marks]

Basic Understanding of Sin, Cos, Tan, Sec, Cosec and Cot Graph

1. Sketch

Example:

1. Sketch graph y = 3 sin 2x2. Sketch graph y = -4 tan x

3. Sketch graph y = |3 cos x|

Exercise:1. Sketch graph y = 3 cosec 2x 22. Sketch graph y = - cot x

Example:

1. (a) Sketch graph y = - 3 cos x for 0 < x < 2

(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

3 cos x = -2x for 0 < x < 2. Then, state the number of solutions2. (a) Sketch graph y = 2 sin 3 x for 0 < x < 2

2

(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

x - 2 sin x = 0 for 0 < x < 2. Then, state the number of solution3. (a) Sketch graph y = |tan x |for 0 < x < 2 (b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

|2 tan x|- 5 = -2x for 0 < x < 2. Then, state the number of solutions

Exercise:

1. (a) Sketch graph y = |4 cos x | for 0 < x < 2

(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

|4 cos x | + x = 2 for 0 < x < 2. Then, state the number of solutions

2. (a) Sketch graph y = 1 sin x for 0 < x < 2

2

(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

sin x = 1 - x for 0 < x < 2. Then, state the number of solutions 2 2(a) Sketch graph y = cos 2x for 0 < x < 2

(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation

2 cos 2x = 1 - x for 0 < x < 2. Then, state the number of solutions Paper 1 [1 or 2 questions, 4 8 marks]PATTERN #1: Solve the following trigonometric function below for 0 < x < 360(a) sin x = 0.1234

(b) cot x = 0.5678

(c) cos x = 0.3456

(d) sec x = 0.6789PATTERN #2: Solve the following trigonometric function below for 0 < x < 360(a) cos x = - 0.9876

(b) cosec x = - 0.5432(c) tan x = - 0.7654

(d) cot x = - 0.3219PATTERN #3: Solve the following trigonometric function below for 0 < x < 360(a) 5 tan x = - 3.4567

(b) sec x = 0.5432(c) 0.8 sin x = 0.12

(d) 7 cot x = 6

PATTERN #4: Solve the following trigonometric function below for 0 < x < 360(a) sin 2x = - 0.4567

(b) cos 2x = 0.5432(c) 3 tan 2x = 0.6789

(d) 12 sec 2x = -6

PATTERN #5: Solve the following trigonometric function below for 0 < x < 360(a) sin x = - 0.4567

(b) cos x = 0.1234(c) 3 tan x = - 0.6789

(d) 12 sec x = -18PATTERN #6: Solve the following trigonometric function below for 0 < x < 360(a) cos (x + 50) = 0.9876

(b) cosec (2x - 10) = 0.5432(c) 2 tan (x + 40) = 1.7654

(d) cot (x + 25) = 0.3219

PATTERN #7: Solve the following trigonometric function below for 0 < x < 360(a) cos 2 x = 0.9876

(b) cosec 2 2x = 0.5432(c) 2 tan 2 x = 2.7654

(d) cot 2 x = 0.3219

PATTERN #8: Solve the following trigonometric function below for 0 < x < 360(a) 2tan 2 x + tan x -3 = 0

(b) 6 sin 2 x + sin x - 2 = 0(c) 2 cos 2 x + 5 cos x - 3 = 0

(d) 15 sin 2 x = sin x + 4 sin 30

PATTERN #9: Solve the following trigonometric function below for 0 < x < 360(a) cos 2 x - cos x + 1= sin 2 x

(b) cot 2 x cosec x = 1(c) 2 cos 2 x = 3 sin x

(d) 2 sin x = 3 cos 2 x - 2PATTERN #10: (i) Given that sin A = and sin B = where A lies on 0 < A < 90 and B lies on 90 < B < 180 respectively. Find (a) sin (A + B)

(b) sec (A + B)(c) tan (A - B)

(d) cosec (A B)(e) cos (A + B)

(f) cot (A + B)(ii) Given that tan V = - and cos W = - where A lies on 270 < V < 360 and lies on 90 < W < 180 respectively. Find:(a) sin (V + W)

(b) sec (W + V)(c) tan (W - V)

(d) cosec (V W)

(e) cos (V + W)

(f) cot (W - V)PATTERN #11: (i) Given that sin A = - p where p lies on the fourth quadrant(a) cos A

(b) sec A(c) tan A

(d) cosec A(e) cos 2A

(f) sec 2A(g) tan 2A

(h) cosec 2A

(i) cos A

(j) sec A(k) tan A

(l) cosec A

(ii) Given that tan V = r and V lies on quadrant before second quadrant(a) sin V

(b) sec V(c) cot V

(d) cosec V

(e) cos 2A

(f) sec 2A(g) tan 2A

(h) cosec 2A

(i) cos V

(j) sec V(k) tan V

(l) cosec V

Trial SPM Perak 2012 [7 marks]

Trial SPM Negeri Sembilan 2013 [7 marks]

Trial SPM Perak 2013 [7 marks]

Trial SPM MRSM 2013 [7 marks]

Trial SPM MRSM 2010 [7 marks]

Trial SPM Negeri Sembilan 2010 [7 marks]

Cikgu Zaidi J-dai 2014, Hak Cipta Terpelihara 1 | Page

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