SPRINGFIELD SCHOOL
1
Academic Year 2024 - 2025
G9 A-Math – Worksheet – Trigonometry
Answer
Key
Name / Class:.............................
Assumed Knowledge
Check the two triangles below, one is an halve of equilateral triangle and the other one is an isosceles rightangled triangle. Put the simplest ratio on each side of the two triangles.
⑮
#
2
53
1
-
/60o
.
7
E
=
1945
↓
I
Complete the table of trigonometry ratio of special angles in Quadrant 1 below:
0o / 0
Sin
!
45o / #
I
Tan
O
!
!
60o / $
90o / %
-
↳
O
Cos
!
30o / "
-
=
I
g
E
O
Angles in any magnitude.
In degrees:
In radians:
= 1 57
goo
1889
.
O
O
T = 3 14
G
.
2T =
3600
2788
3
=
4 7
.
6 28
.
SPRINGFIELD SCHOOL
Academic Year 2024 - 2025
2
Notes:
~ One of the arms of the angle is always the &-axis positive.
=
~
~
Basic / Reference angles are acute and positive angles. Therefore, all angles in quadrant 1 are also
the reference angle.
Positive angles are measured from &-axis positive (0o) to anticlockwise direction.
Negative angles are measured from &-axis positive (0o) to clockwise direction.
1. Draw angles in any Quadrants (sketch only without protractor).
a. Quadrant 1:
a. 30o
b. 72o
oso
hel
30
Ref
Ref
=
b. Quadrant 2: (Also show its reference angle).
a. 135o
It
Ref
=
I do
450
Ref
c. Quadrant 3: (Also show its reference angle).
a. 200o
x
↑
Ref
b. 160o
=
20
=
20
b. 250o
pi
Ref
=
70
%
=
72
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Academic Year 2024 - 2025
3
d. Quadrant 4: (Also show its reference angle).
a. 290o
y
y
Ref
=
b. 348o
70
Ref
%
12
=
2. Draw the angles given (now in radians), indicate also the reference angle of each angle.
a. 2 radians
1
.
b. 4 radians
57
it
:
an
Ref
=
1
.
1
pi)
Ref
4 71
.
c. 6 radians
0
=
.
86
d. 3.5 radians
pin
&Y
Ref
e. 4.25 radians
·
=
0
.
28
Ref
=
0
.
36
f. 5 radians
Qu
Ref
=
1 28
.
SPRINGFIELD SCHOOL
Academic Year 2024 - 2025
4
g. 1 radian
h. 1.5 radians
let
!
Ref
Ref =
1 5
=
.
3. Draw the angles given (negative angles), indicate also the reference angle of each angle.
-
a. - 450
-
b. - 1 radians
2700
=
47
-
.
-100-
Ref
gu
=
%
c. - 1200
=
-
Ref
1 57
.
=
d. - 2.5 radians
"
↑%120
-
=
e. – 2500
2508
=
60
Ref
=
0
f. - 4 radians
Wit
Hig
Ref
2 5
.
Ref
-
-
45
°
70
Ref
=
0
.
86
.
64
1
SPRINGFIELD SCHOOL
Academic Year 2024 - 2025
5
g. – 3300.
h. - 5.8 radians
-
G
·
Ref
=
-
-
3
.
2π
=
-
4 7)
.
14 D
-
300
Rej
=
0
.
For all positive angles, complete the table below:
Reference
Quadrant 1
Quadrant 2
1800
ref
-
0
45
450
0
23
58
180
600
600
300
3ga
ref
come
720
180
-
a
tae
is
588
720
ref
Quadrant 4
3600
-
230
0
Quadrant 3
180 +
The Trigonometric Ratios for angle in any magnitude.
Complete the table below: (correct into 3 SF)
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
Trig Ratio
500
1300
2300
3100
Sin
0 766
0 766
Cos
. 643
0
Tan
1
.
19
0 766
-
.
.
-
0 643
0 643
-
.
.
-
Do you notice something special from the table?
1
.
19
-
0 766
.
.
1
.
19
0
-
.
1
643
.
19
SPRINGFIELD SCHOOL
Academic Year 2024 - 2025
6
Complete again the table below: (correct into 3 SF)
Trig Ratio
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
640
1530
2200
3250
-ente
Sin
Cos
this
Tan
table
by
your
self
Do you find the same patterns of the signs of the trigonometric ratios?
Summary:
+
S
-
-
-
T
-
↑
Sin
Cos
Qz
Q
Q3
Q4
Tan
Sin
Sin
+
Cos
+
A
Tant
Sin-
Cos
Cost
Tan
Tan-
REMEMBEREQ
,
Add
Q2
Q
Q4
Sugar To Coffee
C
SPRINGFIELD SCHOOL
Academic Year 2024 - 2025
7
Complete the table below: (correct to 1 dp)
Ratio
sin * =
Possible Quadrants
1
2
Q , Q2
1
2
Q2 & Q3
cos * = −
tan * =
1
2
cos * = 0.286
tan * = −1.5
sin * = −0.732
Q Q3
Q , Q4
Q2 & Q4
Q3Q4
1st angle
2nd angle
300
3ga
150"
cos" (2)
1280
2480
Reference Angle
0 =
Sin" (2)
o =
600
=
tan" (E)
26
60
.
73 40
.
tan" (1
56
.
5)
.
38
sin-1 (0 732)
26
60
.
.
73 4286
6
.
.
70
70
303
10
312 go
1st angle
2nd angle
123
.
.
47 10
206 60
227
.
.
.
.
What if All Positive Angles are in Radians? (correct to 3SF)
Ratio
sin * =
Possible Quadrants
Reference Angle
3
4
Qia Q2
0 848
4
9
Q2Q3
cos * = −
tan * =
1
3
cos * = 0.741
tan * = −1.8
sin * = −0.123
.
1
.
1
0
.
848
2 03
.
2
.
29
4 25
.
theremain
delete
its
table