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Trigonometry Questions & Solutions - Past Papers
NOVEMBER 2008
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QUESTION 10
10.1
10.2
If sin 28° = a and cos 32°= b, determine the following in terms of a and/or b :
10.1.1
cos 28
(2)
10.1.2
cos64
(3)
10.1.3
sin 4°
(4)
Prove without the use of a calculator, that if sin 28° = a and cos 32° = b, then
b 1  a2  a 1 b2 
10.3
1
.
2
(4)
Evaluate each of the fo llo wing without using a calculator. Show ALL working.
10.3.1
sin 130. tan 60
cos 540. tan 230. sin 400
(7)
10.3.2
(1  2 sin 75)( 2 sin 75  1)
(4)
10.4
Determine the general solution of: sin x  cos 2 x  cos x  0
(7)
10.5
Consider:
2
cos 2 x. tan x
sin 2 x
10.5.1
For wh ich values of x, x  [0 ; 180] , will this exp ression be undefined?
10.5.2
Prove that
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(3)
cos 2 x. tan x cos x

 tan x for all other values of x.
sin x
sin 2 x
(5)
[39]
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QUESTION 11
The sketch below shows one side of the elevation of a house. Some dimensions (in metres) are
indicated on the figure.
E
7,5
D
32
C
G
3,5
A
F
B
9,4
Calculate, rounded off to ONE decimal place:
11.1
EC
(3)
11.2
DĈE
(3)
11.3
Area of  DEC
(2)
11.4
The height EF
(3)
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QUESTION 12
The graph of f ( x)  2 sin x is drawn below.
y
2
f
1
x
-180
-150
-120
-90
-60
-30
30
60
90
120
150
180
-1
-2
12.1
Write down the period of f.
12.2
Write down the amplitude of h if h (x ) 
12.3
Draw the graph of g ( x )  cos(x  30) for x  [180 ; 180] on the grid provided on
DIA GRAM SHEET 5.
12.4
Use
the
graph
to
determine
(1)
the
f (x )
.
4
number
(2)
of
solutions
for
(3)
 2 sin x  cos(x  30) ,
x  [ 180 ; 180] .
(1)
12.5
For wh ich values of x is g(x)  0?
(2)
12.6
For wh ich values of x is
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f / ( x)  0 and g / ( x)  0 ?
(3)
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***** SOLUTIONS TO FOLLOW *****
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