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TRIGONOMETRY
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TRIGONOMETRY
BY
AIRIL BIN AHMAD
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Trigonometry - Introduction
Opposite side
Adjacent side
Hypotenuse
Adjacent side
Opposite side
Hypotenuse
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Sunday, July 07, 2013
Trigonometry - Introduction
Adjacent side
Opposite side
Hypotenuse
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Sunday, July 07, 2013
Trigonometry - Exercise
Name the side of the right angle
triangle given below.AB
C
1.
AB=
BC=
AC=
AB
C
2.
AB=
BC=
AC=
Adjacent
Opposite
Hypotenuse
Opposite
Adjacent
Hypotenuse
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Sunday, July 07, 2013
Trigonometry - Exercise
AB
C
3.
AB=
BC=
AC=
AB
C
4.
AB=
BC=
AC=
OppositeHypotenuse
Adjacent
Hypotenuse
Adjacent
Opposite
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Sunday, July 07, 2013
Trigonometry - Exercise
YZ
X
5.
XY=
YZ=
XZ=
Y
Z
X
6.
XY=YZ=
XZ=
Opposite
Hypotenuse
Adjacent
HypotenuseOpposite
Adjacent
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Sin x0= Opposite
Hypotenuse
AB
C
1.
x0
Opposite
Adjacent
HypotenuseSin x0= BC
AC
Trigonometry Sin , Cos and Tan
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Sunday, July 07, 2013
Cos x0= Adjacent
Hypotenuse
AB
C
1.
x0
Opposite
Adjacent
HypotenuseCos x0= AB
AC
Trigonometry Sin , Cos and Tan
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Sunday, July 07, 2013
Tan x0= Opposite
Adjacent
AB
C
1.
x0
Opposite
Adjacent
HypotenuseTan x0= BC
AB
Trigonometry Sin , Cos and Tan
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Trigonometry Sin , Cos and Tan
Tan x0= Opposite
Adjacent
Sin x0= Opposite
Hypotenuse
Cos x0= Adjacent
Hypotenuse
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Sunday, July 07, 2013
Trigonometry Sin , Cos and Tan
LEE PENG SAN
TONG SAM PAH
SOH CAH TOA
HANG LI PO
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Sunday, July 07, 2013
Trigonometry Sin , Cos and Tan
S O HC A H
T O A
in pposite ypotenuse
os djacent ypotenuse
an pposite djacent
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Trigonometry Sin , Cos and Tan
3 4 55 12 136 8 107 24 25
8 15 179 12 15
10 24 2612 16 20
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Sunday, July 07, 2013
Trigonometry - Exercise
Find the value of sin, cos and tan from the given triangle.
1. AB
C Sin x0 =
Cos x0=
Tan x0=
x0AB
C
2.
x0
Sin x0 =
Cos x0=
Tan x0=
BC/AC
AB/AC
BC/AB
AB/AC
BC/AC
AB/BC
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Sunday, July 07, 2013
Trigonometry - Exercise
Find the value of sin, cos and tan from the given triangle.
3. QP
R
Sin x0 =
Cos x0=
Tan x0=
x0
E
FG
4.
x0
Sin x0 =
Cos x0=
Tan x0=
P/R
Q/R
P/Q
G/E
F/E
G/F
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Sunday, July 07, 2013
Trigonometry - Exercise
Find the value of sin, cos and tan from the given triangle.
5. 3
4
5
Sin x0 =
Cos x0=
Tan x0=
x0
6
8
6.
x0
Sin x0 =
Cos x0=
Tan x0=
4/5
3/5
4/3
6/10 = 3/5
8/10 = 4/5
6/8 = 3/4
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TRIGONOMETRY
BY
AIRIL BIN AHMAD
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Trigonometry - Exercise
1. Find the length of PR
and sin y0
2. Find the length of AB
and cos A
y0
1. PR= 8cm
Sin y= 3/8
2. AB= 13cm
Cos A= 12/13
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Trigonometry - Exercise3. Find sin y0
and cos y04. Find sin x0
4cm
10cm 17 cm
1. Sin y= 8/17
2. Sin x= 7/ 25
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Trigonometry - Exercise
5. If cos x0 = 3/5. Find sin y0 6. Find sin y0
1. Sin y= 6/13
2. Sin y= 8/17
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Trigonometry - Exercise
8. Given that sin x0=8/10 andthe length of PR = 21cm , find
cos y0
y0
7. In the diagram, PQR and TSQ are straightlines. Given that tan x0 =6/9 and S is
the midpoint of TQ, find the length of PT andsin y0
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Trigonometry - Exercise
9. In the figure, QS=8cm, find tan x0
S
RX0
Q
5
T
P9
5
P
7
S
RQ
T
X0
10. In the figure, Find sin x0
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TRIGONOMETRY
BY
AIRIL BIN AHMAD
Sunday July 07 2013
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TRIGONOMETRY
Example 1
ABC is a right angle triangle. Given that tan y0 = 3 / 4, find the length of x and
sin y0
A
C
B 12
Y0
X3
4x 3 =
x
3
=
9
9
= 15
Sin y0 = Opposite
Hypotenuse
= 9 = 3
15 5
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TRIGONOMETRY
Example 2
ABC is a right angle triangle. Given that tan y0 = 3 / 4, find the length of x and
sin y0
A
C
B 16
Y0
X3
4x 4 =
x
4
=
12
12
= 20
Sin y0 = Opposite
Hypotenuse
= 12 = 3
20 5
5 X 4 = 20
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TRIGONOMETRY
Exercise 1
ABC is a right angle triangle. Given that tan y0 = 5 / 12, find the length of x and
sin y0
A
C
B 24
Y0
X
X = 26
Sin y0 = Opposite
Hypotenuse
= 10 = 5
26 13
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y, y ,
TRIGONOMETRY
Exercise
1. In the diagram, PQRS is a rectangle. RST and QT are straight lines.
Given that tan x = . Find sin y , cos y and tan y.
ANSWER:
Sin y = 8/17
cos y = 15/17
Tan y = 8/15
x
3
4
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y, y ,
TRIGONOMETRY
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TRIGONOMETRY
EXERCISE
BY
AIRIL BIN AHMAD
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y y
TRIGONOMETRY
Exercise
1. In the diagram, PQRS is a rectangle. RST and QT are straight lines.
Given that tan x = . Find sin y , cos y and tan y.
ANSWER:
Sin y = 8/17
cos y = 15/17
Tan y = 8/15
x
3
4
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In the diagram, S is the midpoint ofPQ.
If tanx= and PR= 10 cm, then tan y=5
2
QUESTION NO.1
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QUESTION NO.2
In the diagram, EFG and GHIare straight lines.If tanx= 2, then tan y=
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QUESTION NO.3
8
3In the diagram, sinx= . The value ofyis
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QUESTION NO.4
In the diagram, find the value of sin .
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QUESTION NO.5
In the diagram, sin t=5
4
. Find the value ofx.
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QUESTION NO.6
In the diagram, the value of cosxis
24
25
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QUESTION NO.7
5
3In the diagram, LMNand PNQ are straightlines. If cosx= ,then find tan y.
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QUESTION NO.8
12
5
In the diagram, tanx= , find value of cos y.
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QUESTION NO.9
Given that tan 42 = 0.9, sin 42 = 0.67and cos 42 = 0.74.
Calculate the height, in m,
of the tree shown in the diagram
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QUESTION NO.10
The diagram shows a kite flying in the sky.Given that tan 75 = 3.7, sin 75 = 0.97
and cos 75 = 0.26.
Find the value oft.
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QUESTION NO.11
The diagram shows a flagpole that issupported by a wire QR.
Find the angle ofPRQ, in degree.
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QUESTION NO.12
114
13
5In the diagram, KLMis a straight line.Given that tanx = and sin y=Calculate the length,
in cm, ofLM.
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QUESTION NO.13
5
3In the diagram, GMHand MFNare straight lines. If sinx =
then find the value of tan y.
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QUESTION NO.14
The diagram shows a rectangle PQRS.Mis the midpoint ofRS.
Find the value of cosx.
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QUESTION NO.15
5
3In the diagram, JMKis a straight line.Given that sinx = . Find the value of tan y.
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QUESTION NO.16
5
4
In the diagram, Mis themidpoint ofQR.
Given that cos y =
find the value of tanx.
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QUESTION NO.17
In the diagram, HJK and JML are straight lines.Find the value of cos y.
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QUESTION NO.18
In the diagram,find the value of
tan B and cos B.
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QUESTION NO.19
5
6In the diagram, FJMPis a rectangle.JKS and PKMare straight lines. If tanx =then find the value of sin y.
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QUESTION NO.21
13
12In the diagram, HJMand JPTare straight lines.Given that cosx = , find the value of tan yo.
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QUESTION NO.22
25
24
Based on the diagram, cosx = , find FG.
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QUESTION NO.23
13
5In the diagram, PRMS is a straight line.Mis the midpoint ofRS. Given that sinx =find the length ofPR, in cm.
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QUESTION NO.24
4
3
In the diagram, PSTand QTRare straight lines.
S is the midpoint ofPT.
Given that tan y =find the length ofPQ.
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QUESTION NO.25
The diagram shows a square HJQS.Find the value of sinx.
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QUESTION NO.26
5
3In the diagram, PQRis a straight line.If sinx = , then find the value of tan y.
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QUESTION NO.27
In the diagram, JPKis a straight line.Given that JP= 7 cm,
calculate the value of tanx.
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30cm
QUESTION NO.28
5
3In the diagram, PQRis a straight line.Given that sinx = . Find the length ofPR.
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QUESTION NO.29
B
M
CA
x
25
7
In Diagram 13, Mis the midpoint ofBCin a right-angled triangleABC.
Given that cosx=
Find the lengthofMC.
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7 m
24 m
QUESTION NO.30
In Diagram 9, a long pole isplaced against a wall.
The wall is 7 m high and
the foot of the pole is 24m
away from the foot of the wall.Calculate the length, in m,
of pole that is jutting over
the wall (x), if the pole is
35 metres long.
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TRIGONOMETRY(Using Calculator)
BY
AIRIL BIN AHMAD
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TRIGONOMETRY
1 degree (10) = 60 min (600) 10=60
Example 1
Change the angle in degreesto degrees and minutes.
a. 30.80
b. 15.30
c. 28.50
d. 50.90
On your calculator
1. Press 30.8
2. Press 0,,,
3. Press =
The value obtained is30048
= 150 18
= 280 30
= 500 54
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TRIGONOMETRYExercise
Change the angle in
degrees to degrees and
minutes.a. 37.80
b. 95.30
c. 68.50
d. 59.10
e. 46.90
Exercise
f. 79.90
g. 15.150
h. 30.650
i. 47.250
j. 9.550
k. 36.450
l. 80.350
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TRIGONOMETRY
Example 2
Change the angle in degrees
and minutes to degrees
a. 300 18
b. 360 36
c. 670
54
d. 62051
On your calculator
1. Press 30
2. Press 0,,,
3. Press 18
4. Press 0,,,5. Press =
6. Press 0,,,
The value obtained is30.3
= 36.6
= 67.9
= 62.85
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TRIGONOMETRYExercise
Change the angle in
degrees and minutes to
degrees.a. 30027
b. 15054
c. 28024
d. 50012
e. 36008
Exercise
f. 79023
g. 150 42
h. 300 51
i. 47017
j. 90 9
k. 360
24
l. 80033
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TRIGONOMETRYExercise
Find the value of:
a. Sin 30027
b. tan 15054
c. cos 28024
d. cos 50012
e. sin 360
08
Exercise
f. tan 79023
g. tan 150 42
h. sin 300 51
i. cos 47017
j. Tan 90 9
k. cos 360
24
l. sin 80033
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TRIGONOMETRYExample 4
Using calculator to find the value of
the angle
a. Sin = 0.5925
b. Cos = 0.5925
c. Tan = 0.9342
d. Sin = 0.2479
e. Sin = 0.7992f. Cos = 0.3345
On your calculator
1. Press shift
2. Press sin
3. Press 0.5925
4. Press =
The value obtained is
36.33460
5. Press 0
The value is 36020
= 53039
= 43003
= 14021
= 53003
= 70027
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TRIGONOMETRY
Exercise
Find the value of:
a. Sin = 0.8025
b. Cos = 0.2925
c. Tan = 1.8942
d. Sin = 0.0679
e. Sin = 0.9292
f. Cos = 0.0445
Exercise
g. Tan = 0.1234
h. Sin = 0.4425
i. Cos = 0.5925j. Tan = 2.9342
k. Sin = 0.5579
l. Sin = 0.0009m. Cos = 0.7945
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TRIGONOMETRY
Example 5
Find the angle of y0
6cm
A
CB
Y0
10cm
Solution
Sin y0 = Opposite
hypotenuse
sin y0 = 6 = 0.6
10
y = 360 52#
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TRIGONOMETRY
Example 6
Find the angle of y0
9cm
A
CB
Y0
15cm
Solution
Cos y0 = Adjacent
hypotenuse
cos y0 = 9 = 0.6
15
y = 530 07#
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TRIGONOMETRY
Exercise
1. Find the angle of y0
Exercise
2. Find the angle of y0
A
5cm
CB
Y0
8cm
7cm
A
CB
Y0
11cm
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TRIGONOMETRY
Exercise
3. Find the angle of y0
Exercise
4. Find the angle of y0
4cm
A
CB
Y0
9cm
3cm
A
CB
Y0
7cm
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TRIGONOMETRY
Exercise
5. Find the angle of y0
Exercise
6. Find the angle of y0
6cm
A
CB
Y0
13cm
8cm
A
CB
Y0
11cm
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TRIGONOMETRY
Example 7
Find the length of x
X
A
CB
300
7cm
Solution
Sin 300 = Opposite
hypotenuse
sin 300 = x
7
0.5 = x
7x = 0.5 x 7
x = 3.5cm
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TRIGONOMETRY
Example 8
Find the length of x
X
A
CB
35027
6cm
Solution
Sin 35027 = Opposite
hypotenuse
sin 35027 = x
6
0.5800 = x
6x = 0.5800 x 6
x = 3.48cm
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TRIGONOMETRY
Exercise
1. Find the length of x
Exercise
2. Find the length of x
A
x
CB
600
12cm
x
A
CB
58045
15cm
X=10.39 X=12.82
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TRIGONOMETRY
Exercise
3. Find the length of x
Exercise
4. Find the length of x
x
A
CB
27019
7cm
x
A
CB
61023
13cm
X=6.22 X=6.23
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TRIGONOMETRY
Exercise
5. Find the length of x
Exercise
6. Find the length of x
x
A
CB
52050
13cm
x
A
CB
48025
8cm
X=17.15 X=9.02
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QUESTION NO.9
Given that tan 42 = 0.9, sin 42 = 0.67and cos 42 = 0.74.
Calculate the height, in m,
of the tree shown in the diagram
Question 7
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QUESTION NO.11
The diagram shows a flagpole that issupported by a wire QR.
Find the angle ofPRQ, in degree.
Question 9
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10. A ladder makes an angle of 650 with a
wall when it reaches a height of 10m. up thewall. How far is the foot of the ladder away
from the wall?
11. A straight road 240m long rises 120m
vertically from one end to the other. Find the
angle between the road and the horizontal.
10m
650
120m