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

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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.

Adjacent

Opposite

Hypotenuse

Opposite

Adjacent

Hypotenuse

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Opposite

Hypotenuse

Adjacent

Hypotenuse

Adjacent

Opposite

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Opposite

Hypotenuse

Adjacent

Hypotenuse

Opposite

Adjacent

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Sin x0= Opposite

Hypotenuse

Opposite

Adjacent

Hypotenuse Sin x0= BC

Trigonometry – Sin , Cos and Tan

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Cos x0= Adjacent

Hypotenuse

Opposite

Adjacent

Hypotenuse Cos x0= AB

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Tan x0= Opposite

Adjacent AB

Opposite

Adjacent

Hypotenuse

Tan x0= BC

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Tan x0= Opposite

Adjacent

Sin x0= Opposite

Hypotenuse

Cos x0= Adjacent

Hypotenuse

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LEE PENG SAN

TONG SAM PAH

SOH CAH TOA

HANG LI PO

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in pposite ypotenuse

os djacent ypotenuse

an pposite djacent

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

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

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

C Sin x0 =

Cos x0 =

Tan x0 =

Sin x0 =

Cos x0 =

Tan x0 =

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

Sin x0 =

Cos x0 =

Tan x0 =

Sin x0 =

Cos x0 =

Tan x0 =

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

Sin x0 =

Cos x0 =

Tan x0 =

Sin x0 =

Cos x0 =

Tan x0 =

6/10 = 3/5

8/10 = 4/5

6/8 = 3/4

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TRIGONOMETRY

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1. Find the length of PR

and sin y0

2. Find the length of AB and cos A

1. PR= 8cm

Sin y= 3/8

2. AB= 13cm

Cos A= 12/13

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3. Find sin y0

and cos y04. Find sin x0

10cm17 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 and the length of PR = 21cm , find cos 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

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

10. In the figure, Find sin x0

Wednesday, April 12, 2023 AIRIL BIN AHMAD

TRIGONOMETRY

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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

4 x 3 =

Sin y0 = Opposite

Hypotenuse

= 9 = 3

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TRIGONOMETRY

Example 2

4 x 4 =

Sin y0 = Opposite

Hypotenuse

= 12 = 3

5 X 4 = 20

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TRIGONOMETRY

Exercise 1

X = 26

Sin y0 = Opposite

Hypotenuse

= 10 = 5

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TRIGONOMETRY

Exercise 2

X = 40

Sin y0 = Opposite

Hypotenuse

= 18 = 3

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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

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TRIGONOMETRY

TRIGONOMETRY EXERCISE

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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

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In the diagram, S is the midpoint of PQ.

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

QUESTION NO.1

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

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QUESTION NO.3

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

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

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QUESTION NO.5In the diagram, sin t =

4. Find the value of x.

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

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QUESTION NO.7

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

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QUESTION NO.8

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

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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

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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.

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

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QUESTION NO.12

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

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QUESTION NO.13

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

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

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QUESTION NO.15

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

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QUESTION NO.16

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

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

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

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QUESTION NO.19

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

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

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QUESTION NO.21

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

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QUESTION NO.22

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

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QUESTION NO.23

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.

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QUESTION NO.24

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

find the length of PQ.

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

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QUESTION NO.26

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

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

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QUESTION NO.28

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

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QUESTION NO.29

50 cm25

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

= Find the lengthof MC.

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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.

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TRIGONOMETRY(Using Calculator)

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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

Solution

Sin y0 = Opposite hypotenuse

sin y0 = 6 = 0.6 10

y = 360 52’#

TRIGONOMETRYExample 6Find the angle of y0

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

TRIGONOMETRYExample 7Find the length of x

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

350 27’

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

58045’

X=10.39 X=12.82

27019’

61023’

X=6.22 X=6.23

52050’

48025’

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.

NOTE MATH FORM 3 - 15 trigonometry

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