NOTE MATH FORM 3 - 15 trigonometry

Wednesday, April 12, 2023

AIRIL BIN AHMAD

TRIGONOMETRY


AIRIL BIN AHMAD

TRIGONOMETRY

BY AIRIL BIN AHMAD


AIRIL BIN AHMAD

Trigonometry - Introduction

Opposite side

Adjacent side

Hypotenuse

Adjacent side

Opposite side

Hypotenuse


AIRIL BIN AHMAD

Trigonometry - Introduction

Adjacent side

Opposite side

Hypotenuse


AIRIL BIN AHMAD

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


AIRIL BIN AHMAD


AB

C

3.

AB=

BC=

AC=

AB

C

4.

AB=

BC=

AC=

Opposite

Hypotenuse

Adjacent

Hypotenuse

Adjacent

Opposite


AIRIL BIN AHMAD


YZ

X

5.

XY=

YZ=

XZ=

Y

Z

X6.

XY=

YZ=

XZ=

Opposite

Hypotenuse

Adjacent

Hypotenuse

Opposite

Adjacent


AIRIL BIN AHMAD

Sin x0= Opposite

Hypotenuse

AB

C

1.

x0

Opposite

Adjacent

Hypotenuse Sin x0= BC

AC

Trigonometry – Sin , Cos and Tan


AIRIL BIN AHMAD

Cos x0= Adjacent

Hypotenuse

AB

C

1.

x0

Opposite

Adjacent

Hypotenuse Cos x0= AB

AC



AIRIL BIN AHMAD

Tan x0= Opposite

Adjacent AB

C

1.

x0

Opposite

Adjacent

Hypotenuse

Tan x0= BC

AB



AIRIL BIN AHMAD


Tan x0= Opposite

Adjacent

Sin x0= Opposite

Hypotenuse

Cos x0= Adjacent

Hypotenuse


AIRIL BIN AHMAD


LEE PENG SAN

TONG SAM PAH

SOH CAH TOA

HANG LI PO


AIRIL BIN AHMAD


S O H

C A H

T O A

in pposite ypotenuse

os djacent ypotenuse

an pposite djacent


AIRIL BIN AHMAD


3 4 5 5 12 13 6 8 10 7 24 25

8 15 17 9 12 15 10 24 26 12 16 20


AIRIL BIN AHMAD


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


AIRIL BIN AHMAD


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


AIRIL BIN AHMAD


Find the value of sin, cos and tan from the given triangle.5. 3

45

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


AIRIL BIN AHMAD

TRIGONOMETRY

BY

AIRIL BIN AHMAD


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


AIRIL BIN AHMAD


3. Find sin y0

and cos y04. Find sin x0

4cm

10cm17 cm

1. Sin y= 8/17

2. Sin x= 7/ 25


AIRIL BIN AHMAD


5. If cos x0 = 3/5. Find sin y0 6. Find sin y0

1. Sin y= 6/13

2. Sin y= 8/17


AIRIL BIN AHMAD


8. Given that sin x0= 8/10 and the length of PR = 21cm , find cos y0

y0

7. In the diagram, PQR and TSQ are straight lines. Given that tan x0 =6/9 and S is the midpoint of TQ, find the length of PT and sin y0


AIRIL BIN AHMAD


9. In the figure, QS=8cm, find tan x0

S

RX0

Q

5

T

P9

5

P7

S

RQ

T

X0

10. In the figure, Find sin x0

Wednesday, April 12, 2023 AIRIL BIN AHMAD

TRIGONOMETRY

BY

AIRIL BIN AHMAD

AIRIL BIN AHMAD


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

CB 12

Y0

X3

4 x 3 =

x

3

=

9

9

= 15

Sin y0 = Opposite

Hypotenuse

= 9 = 3

15 5

AIRIL BIN AHMAD


TRIGONOMETRY

Example 2


A

CB 16

Y0

X3

4 x 4 =

x

4

=

12

12

= 20

Sin y0 = Opposite

Hypotenuse

= 12 = 3

20 5

5 X 4 = 20

AIRIL BIN AHMAD


TRIGONOMETRY

Exercise 1


A

CB 24

Y0

X

X = 26

Sin y0 = Opposite

Hypotenuse

= 10 = 5

26 13

AIRIL BIN AHMAD


TRIGONOMETRY

Exercise 2


A

CB 24

Y0

X

X = 40

Sin y0 = Opposite

Hypotenuse

= 18 = 3

30 5

AIRIL BIN AHMAD


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

AIRIL BIN AHMAD


TRIGONOMETRY


TRIGONOMETRY EXERCISE

BY

AIRIL BIN AHMAD

AIRIL BIN AHMAD


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

AIRIL BIN AHMAD


In the diagram, S is the midpoint of PQ.

If tan x = and PR = 10 cm, then tan y = 5

2

QUESTION NO.1

AIRIL BIN AHMAD


QUESTION NO.2In the diagram, EFG and GHI are straight lines.If tan x = 2, then tan y =

AIRIL BIN AHMAD


QUESTION NO.3

8

3In the diagram, sin x = . The value of y is

AIRIL BIN AHMAD


QUESTION NO.4In the diagram, find the value of sin θ.

AIRIL BIN AHMAD


QUESTION NO.5In the diagram, sin t =

5

4. Find the value of x.

AIRIL BIN AHMAD


QUESTION NO.6In the diagram, the value of cos x is

24

25

AIRIL BIN AHMAD


QUESTION NO.7

5

3In the diagram, LMN and PNQ are straight lines. If cos x = ,then find tan y.

AIRIL BIN AHMAD


QUESTION NO.8

12

5In the diagram, tan x = , find value of cos y.

AIRIL BIN AHMAD


QUESTION NO.9

Given that tan 42° = 0.9, sin 42° = 0.67 and cos 42° = 0.74. Calculate the height, in m, of the tree shown in the diagram

AIRIL BIN AHMAD


QUESTION NO.10The 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 of t.

AIRIL BIN AHMAD


QUESTION NO.11The diagram shows a flagpole that is supported by a wire QR. Find the angle of PRQ, in degree.

AIRIL BIN AHMAD


QUESTION NO.12

11

4 13

5In the diagram, KLM is a straight line.Given that tan x° = and sin y° = Calculate the length, in cm, of LM.

AIRIL BIN AHMAD


QUESTION NO.13

5

3In the diagram, GMH and MFN are straight lines. If sin x° = then find the value of tan y°.

AIRIL BIN AHMAD


QUESTION NO.14The diagram shows a rectangle PQRS. M is the midpoint of RS. Find the value of cos x°.

AIRIL BIN AHMAD


QUESTION NO.15

5

3In the diagram, JMK is a straight line. Given that sin x° = . Find the value of tan y°.

AIRIL BIN AHMAD


QUESTION NO.16

5

4

In the diagram, M is the midpoint of QR.Given that cos y° = find the value of tan x°.

AIRIL BIN AHMAD


QUESTION NO.17In the diagram, HJK and JML are straight lines. Find the value of cos y°.

AIRIL BIN AHMAD


QUESTION NO.18In the diagram, find the value oftan B° and cos B°.

AIRIL BIN AHMAD


QUESTION NO.19

5

6In the diagram, FJMP is a rectangle. JKS and PKM are straight lines. If tan x° = then find the value of sin y°.

AIRIL BIN AHMAD


QUESTION NO.20In the diagram, PMR is a straight line. M is the midpoint of PR. Find the value of tan D0.

AIRIL BIN AHMAD


QUESTION NO.21

13

12In the diagram, HJM and JPT are straight lines. Given that cos x° = , find the value of tan y o.

AIRIL BIN AHMAD


QUESTION NO.22

25

24Based on the diagram, cos x° = , find FG.

AIRIL BIN AHMAD


QUESTION NO.23

13

5In the diagram, PRMS is a straight line. M is the midpoint of RS. Given that sin x° = find the length of PR, in cm.

AIRIL BIN AHMAD


QUESTION NO.24

4

3

In the diagram, PST and QTR are straight lines. S is the midpoint of PT. Given that tan yº =

find the length of PQ.

AIRIL BIN AHMAD


QUESTION NO.25The diagram shows a square HJQS. Find the value of sin x°.

AIRIL BIN AHMAD


QUESTION NO.26

5

3In the diagram, PQR is a straight line. If sin xº = , then find the value of tan yº.

AIRIL BIN AHMAD


QUESTION NO.27In the diagram, JPK is a straight line. Given that JP = 7 cm, calculate the value of tan xº.

AIRIL BIN AHMAD


30cm

QUESTION NO.28

5

3In the diagram, PQR is a straight line. Given that sin xº = . Find the length of PR.

AIRIL BIN AHMAD


QUESTION NO.29

B

M

CA x

50 cm25

7

In Diagram 13, M is the midpoint of BC in a right-angled triangle ABC. Given that cos x

= Find the lengthof MC.

AIRIL BIN AHMAD


7 m

24 mx

QUESTION NO.30In Diagram 9, a long pole is placed 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.

AIRIL BIN AHMAD


AIRIL BIN AHMAD


TRIGONOMETRY(Using Calculator)

BY

AIRIL BIN AHMAD



TRIGONOMETRY1 degree (10) = 60 min (600) 10=60’

Example 1

Change the angle in degrees to 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 is 300 48’

= 150 18’

= 280 30’

= 500 54’



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



TRIGONOMETRY

Example 2

Change the angle in degrees and minutes to degrees

a. 300 18’

b. 360 36’

c. 670 54’

d. 620 51’

On your calculator

1. Press 30

2. Press 0,,,

3. Press 18

4. Press 0,,,

5. Press =

6. Press 0,,,

The value obtained is 30.3

= 36.6

= 67.9

= 62.85




Change the angle in degrees and minutes to degrees.

a. 300 27’

b. 150 54’

c. 280 24’

d. 500 12’

e. 360 08’

Exercise

f. 790 23’ g. 150 42’

h. 300 51’

i. 470 17’

j. 90 9’

k. 360 24’

l. 800 33’



TRIGONOMETRYExample 3

Use calculator to find the value of sin, cos and tan

a. Sin 300

b. Sin 360 36’c. Cos 670

d. Cos 620 51’e. Tan 350 f. Tan 740 20’

On your calculator

1. Press sin2. Press 30

3. Press 0,,,

4. Press =


= 0.60

= 0.39

= 0.46

= 0.70

= 3.57




Find the value of:a. Sin 300 27’

b. tan 150 54’

c. cos 280 24’

d. cos 500 12’

e. sin 360 08’

Exercise

f. tan 790 23’ g. tan 150 42’

h. sin 300 51’

i. cos 470 17’

j. Tan 90 9’

k. cos 360 24’

l. sin 800 33’



TRIGONOMETRYExample 4

Using calculator to find the value of the angle

a. Sin θ = 0.5925b. Cos θ = 0.5925 c. Tan θ = 0.9342

d. Sin θ = 0.2479 e. Sin θ = 0.7992 f. Cos θ = 0.3345

On your calculator

1. Press shift2. Press sin3. Press 0.59254. Press =


5. Press 0’’’

The value is 360 20’

= 530 39’

= 430 03’

= 140 21’

= 530 03’

= 700 27’



TRIGONOMETRYExerciseFind the value of:a. Sin θ = 0.8025b. Cos θ = 0.2925 c. Tan θ = 1.8942

d. Sin θ = 0.0679 e. Sin θ = 0.9292 f. Cos θ = 0.0445

Exercise g. Tan θ = 0.1234 h. Sin θ = 0.4425i. Cos θ = 0.5925 j. Tan θ = 2.9342

k. Sin θ = 0.5579 l. Sin θ = 0.0009 m. Cos θ = 0.7945



TRIGONOMETRYExample 5Find the angle of y0

6cm

A

CB

Y0

10cm

Solution

Sin y0 = Opposite hypotenuse

sin y0 = 6 = 0.6 10

y = 360 52’#



TRIGONOMETRYExample 6Find the angle of y0

9cm

A

CB

Y0

15cm

Solution

Cos y0 = Adjacent hypotenuse

cos y0 = 9 = 0.6 15

y = 530 07’#



TRIGONOMETRYExercise 1. Find the angle of y0

Exercise 2. Find the angle of y0

A

5cm

CB

Y0

8cm

7cm

A

CB

Y0

11cm





4cm

A

CB

Y0

9cm

3cm

A

CB

Y0

7cm





6cm

A

CB

Y0

13cm

8cm

A

CB

Y0

11cm



TRIGONOMETRYExample 7Find the length of x

X

A

CB

300

7cm

Solution

Sin 300 = Opposite hypotenuse

sin 300 = x 7 0.5 = x 7 x = 0.5 x 7 x = 3.5cm



TRIGONOMETRYExample 8Find the length of x

X

A

CB

350 27’

6cm

Solution

Sin 350 27’ = Opposite hypotenuse

sin 350 27’ = x 6 0.5800 = x 6 x = 0.5800 x 6 x = 3.48cm



TRIGONOMETRYExercise 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





x

A

CB

27019’

7cm

x

A

CB

61023’

13cm

X=6.22 X=6.23





x

A

CB

52050’

13cm

x

A

CB

48025’

8cm

X=17.15 X=9.02



QUESTION NO.9

Given that tan 42° = 0.9, sin 42° = 0.67 and cos 42° = 0.74. Calculate the height, in m, of the tree shown in the diagram

Question 7



QUESTION NO.10The 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 of t.

Question 8



QUESTION NO.11The diagram shows a flagpole that is supported by a wire QR. Find the angle of PRQ, in degree.

Question 9



10. A ladder makes an angle of 650 with a wall when it reaches a height of 10m. up the wall. 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

240

Documents

NOTE MATH FORM 3 - 15 trigonometry