Mathematics Ii

REVISION CHAPTER 1 (from Mid-Semester Exam Sem. II 09/10) 1

 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