# Mathematics Ii

**Topics:**Trigonometry, Trigonometric functions, Periodic function

**Pages:**14 (1560 words)

**Published:**February 6, 2013

2 Given the function : y 2 sin 2x 3 a) Find the i) amplitude ii) period iii) phase shift.

.

b) Sketch the graph of the function over one period.

[6]

2

Find the exact value of the expressions below. Rationalize the denominator where appropriate: a)

cot 70 tan 650 csc( 250 ) sec( 110 ) 5 19 tan cos 6 6 4 23 cot sin 3 6

[5]

b)

[5]

3

a)

From the graph of a sine or cosine curve below,find the equation of the graph in the form of:

(i) (ii)

where where

and and

. .

8

-8

.

[4]

REVISION CHAPTER 2 (from Mid-Semester Exam Sem. II 09/10)

1

Find the exact value of the expressions below. Rationalize the denominator where appropriate: a) b) tan 82.5 tan 52.5

cos 255 cos 195

[6]

2

a) Establish the identity : b)

cot cot 2 csc 2

[5] [4]

If 2sin(x – y) = sin(x + y), prove that tanx = 3tany Given cos10o = p, express the following in terms of p: (i) (ii) (ii) tan10o tan20o cos80o [6]

3

a)

b) 4

Find the exact value of :

4 cos tan 1 1 cos 1 5

[5]

Solve the equation: a)

cos 4 cos 2

Give a general formula for all the solutions. b) 3 cos 4 sin 2 ; 0 360

[6] [7]

5

a) Show that if

then

.

[6]

b)

Prove

.

[4]

6

a)

Given; , , Find the exact value of : (i) Rationalize the denominator where appropriate. [5] .

(ii)

[4]

b) 7

Find the exact value of:

[5]

Solve the equation:

a)

1 sin x cos x 4 cos x 1 sin x

;

0 x 4

[6]

b)

Give the general formula for all the solutions.

[7]

QUESTIONS FROM FINAL MATH 1 FOR CHAPTER 1 AND 2 MATHS 2 1. Without using a calculator, find the exact value of 2. If tan 4 , find the exact value of i) sec2 3. If sin t ii) cot

sin 700 tan 700 0 cos 430

iii) cot 2

8 and the terminal point for t is in quadrant IV , find csc t sec t 17

4. A sinusoidal function is given as y 3 cos 2 x . What is the phase shift? 2 3 5. What is the exact value of sin 1 2

1 6. Given cos , , find the value of each of the remaining trigonometric 3 2 functions. 4 12 7. If sin and cos , in quadrant III and in quadrant IV, what is the 5 13 value of sin ? 8. Show that: i) sin cot tan sec ii) tan2 sin 2 tan2 sin 2

iii) cot

cot cot 1 vi) 1 cos 2 cos 4 cos 6 2sin 3 sin 3 sin cot cot

9. Solve cos 2 5 cos 3 0 , 0 2 10. Find the exact value of a. sec2 520 tan2 520 b. sec 350csc550 –tan350cot550 cos 200 0 c. cot 20 sin 200 11. If sin 0.3 , find the value of sin sin 2 sin 4 1 12. If f cos and f a then find the exact value of f a f a 2 f a 2 4 13. Find the exact value of each of the remaining trigonometric function of if 2 3 sin , 3 2 14. Establish each identity sin 1 cos i) 2 csc 1 cos sin iii) cos cot tan sin cos

ii)

cot tan 1 tan cot 1 tan 1 cot

iv) sin sin sin 2 sin 2

15. Solve the equation on the interval 0 2 , tan 2 2 cos 0 16. Find the exact value of the expression: 4 4 (i) cos tan 1 1 cos 1 (ii) cos 2 tan 1 sin 1 1 3 5 17. If x 2 tan , express cos 2 as a function of x 4 18. Find the exact value of : cos 2 tan 1 3 19. Solve the following equation on the interval 0 2 : sin cos 2 1 sin 3 cos 3 20. Establish the following identity : 1 sin 2 2 sin cos 1 1 21. Given that cos( A B) , sin B , tan A p where p > 0 . Angle A and B 10 10 are in the...

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