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AIRIL BIN AHMAD

Sunday, July 07, 2013

TRIGONOMETRY


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AIRIL BIN AHMAD


TRIGONOMETRY

BY

AIRIL BIN AHMAD


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AIRIL BIN AHMAD


Trigonometry - Introduction

Opposite side

Adjacent side

Hypotenuse

Adjacent side

Opposite side

Hypotenuse


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Trigonometry - Introduction

Adjacent side

Opposite side

Hypotenuse


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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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AIRIL BIN AHMAD



AB

C

3.

AB=

BC=

AC=

AB

C

4.

AB=

BC=

AC=

OppositeHypotenuse

Adjacent

Hypotenuse

Adjacent

Opposite


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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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Cos x0= Adjacent

Hypotenuse

AB

C

1.

x0

Opposite

Adjacent

HypotenuseCos x0= AB

AC



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Tan x0= Opposite

Adjacent

AB

C

1.

x0

Opposite

Adjacent

HypotenuseTan x0= BC

AB






Tan x0= Opposite

Adjacent

Sin x0= Opposite

Hypotenuse

Cos x0= Adjacent

Hypotenuse





LEE PENG SAN

TONG SAM PAH

SOH CAH TOA

HANG LI PO





S O HC A H

T O A

in pposite ypotenuse

os djacent ypotenuse

an pposite djacent





3 4 55 12 136 8 107 24 25

8 15 179 12 15

10 24 2612 16 20





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






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






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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AIRIL BIN AHMAD


TRIGONOMETRY

BY

AIRIL BIN AHMAD


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AIRIL BIN AHMAD



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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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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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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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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AIRIL BIN AHMADSunday, July 07, 2013

TRIGONOMETRY

BY

AIRIL BIN AHMAD

Sunday July 07 2013


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AIRIL BIN AHMAD


Sunday July 07 2013


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AIRIL BIN AHMAD


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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AIRIL BIN AHMAD


TRIGONOMETRY

Example 2


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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AIRIL BIN AHMAD


TRIGONOMETRY

Exercise 1


sin y0

A

C

B 24

Y0

X

X = 26

Sin y0 = Opposite

Hypotenuse

= 10 = 5

26 13


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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

y, y ,

TRIGONOMETRY


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AIRIL BIN AHMADSunday, July 07, 2013

TRIGONOMETRY

EXERCISE

BY

AIRIL BIN AHMAD



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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

QUESTION NO.13

5

3In the diagram, GMHand MFNare straight lines. If sinx =

then find the value of tan y.



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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

QUESTION NO.17

In the diagram, HJK and JML are straight lines.Find the value of cos y.



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AIRIL BIN AHMAD

QUESTION NO.18

In the diagram,find the value of

tan B and cos B.



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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

QUESTION NO.22

25

24

Based on the diagram, cosx = , find FG.



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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

QUESTION NO.25

The diagram shows a square HJQS.Find the value of sinx.



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AIRIL BIN AHMAD

QUESTION NO.26

5

3In the diagram, PQRis a straight line.If sinx = , then find the value of tan y.



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AIRIL BIN AHMAD

QUESTION NO.27

In the diagram, JPKis a straight line.Given that JP= 7 cm,

calculate the value of tanx.



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AIRIL BIN AHMAD

30cm

QUESTION NO.28

5

3In the diagram, PQRis a straight line.Given that sinx = . Find the length ofPR.



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AIRIL BIN AHMAD

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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AIRIL BIN AHMAD

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



66/87

Sunday, July 07, 2013 AIRIL BIN AHMAD

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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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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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


A

5cm

CB

Y0

8cm

7cm

A

CB

Y0

11cm



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TRIGONOMETRY

Exercise


Exercise


4cm

A

CB

Y0

9cm

3cm

A

CB

Y0

7cm



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TRIGONOMETRY

Exercise


Exercise


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


A

x

CB

600

12cm

x

A

CB

58045

15cm

X=10.39 X=12.82



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TRIGONOMETRY

Exercise


Exercise


x

A

CB

27019

7cm

x

A

CB

61023

13cm

X=6.22 X=6.23



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TRIGONOMETRY

Exercise


Exercise


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

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