bengkel trigo 29 julai 2015

TRIGONOMETRY

Wednesday, July 29, 2015TRIGONOMETRI

AIRIL BIN AHMADAIRIL BIN AHMADWednesday, July 29, 2015TRIGONOMETRIOLEH: MOHD FIRDAUS BIN ABDUL WAHAB(cetusan AIRIL BIN AHMAD)

AIRIL BIN AHMADAIRIL BIN AHMADWednesday, July 29, 2015TRIGONOMETRI: -- PENGENALAN

BersebelahAnBertentOnganHipotenus

AIRIL BIN AHMADWednesday, July 29, 2015BersebelahAn

BertentOnganHipotenusTRIGONOMETRI: -- PENGENALANAIRIL BIN AHMADWednesday, July 29, 2015Nyatakan sama ada sisi tersebut adalah bertentangan atau bersebelahan atau hipotenus.ABC1.AB=BC=AC=ABC2.AB=BC=AC=

BersebelahAnBertentOnganHipotenusBersebelahAnBertentOnganHipotenusTRIGONOMETRI LATIHANAIRIL BIN AHMADWednesday, July 29, 2015ABC3.AB=BC=AC=ABC4.AB=BC=AC=

BertentanganHipotenusBersebelahanHipotenusBersebelahanBertentanganTRIGONOMETRI LATIHANAIRIL BIN AHMADWednesday, July 29, 2015

RUMUS!!!Sin x0= Sisi O Sisi H ABC1.x0 Bertenta-ngan Bersebelahan Hipotenus SOHTRIGONOMETRISIN KOS TAN ..AIRIL BIN AHMADWednesday, July 29, 2015

RUMUS!!!kos x0= Sisi A Sisi H

ABC1.x0 Sisi O Sisi A Sisi H TRIGONOMETRISIN KOS TAN ..KAHAIRIL BIN AHMADWednesday, July 29, 2015

tan x0= Sisi O Sisi A ABC1.x0 Bertentangan Bersebelahan hipotenus TOATRIGONOMETRISIN KOS TAN ..AIRIL BIN AHMADWednesday, July 29, 2015

tan x0= Sisi O Sisi A Sin x0= Sisi O Sisi H kos x0= Sisi A Sisi H TRIGONOMETRISOH--- KAH--- TOAAIRIL BIN AHMADWednesday, July 29, 2015

LEE PENG SANTONG SAM PAHSOH KAH TOAHANG LI POTRIGONOMETRISIN KOS TAN ..AIRIL BIN AHMADWednesday, July 29, 2015trigonometri Sin , Cos and Tan

S O H K A H T O A in pposite ypotenuse os djacent ypotenuse an pposite djacent AIRIL BIN AHMADWednesday, July 29, 2015trigonometri Sin , Cos and Tan

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 AHMADWednesday, July 29, 2015trigonometri - Exercise Find the value of sin, cos and tan from the given triangle.

5.345Sin x0 =Cos x0 =Tan x0 =x0686.x0Sin x0 =Cos x0 =Tan x0 =4/53/54/36/10 = 3/58/10 = 4/56/8 = 3/4AIRIL BIN AHMADWednesday, July 29, 2015trigonometri

BY AIRIL BIN AHMAD

AIRIL BIN AHMADAIRIL BIN AHMADWednesday, July 29, 2015trigonometri - Exercise

Find the length of PR and sin y02. Find the length of AB and cos A

y0PR= 8cm Sin y= 3/8

AB= 13cm Cos A= 12/13

AIRIL BIN AHMADWednesday, July 29, 2015trigonometri - Exercise3. Find sin y0 and cos y04. Find sin x0

4cm

10cm17 cmSin y= 8/17

2. Sin x= 7/ 25

AIRIL BIN AHMADWednesday, July 29, 2015trigonometri - Exercise

5. If cos x0 = 3/5. Find sin y06. Find sin y0

Sin y= 6/13

2. Sin y= 8/17

AIRIL BIN AHMADWednesday, July 29, 2015trigonometri - Exercise8. 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 AHMADWednesday, July 29, 2015trigonometri - Exercise9. In the figure, QS=8cm, find tan x0SRX0Q5TP95P7SRQTX010. In the figure, Find sin x0AIRIL BIN AHMADWednesday, July 29, 2015trigonometriBYAIRIL BIN AHMAD

AIRIL BIN AHMADAIRIL BIN AHMADWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 1ABC is a right angle triangle. Given that tan y0 = 3 / 4, find the length of x and sin y0ACB12Y0X34 x 3 = x 3 = 9 9= 15Sin y0 = Bertentangan hipotenus

= 9 = 3 15 5 AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 2ABC is a right angle triangle. Given that tan y0 = 3 / 4, find the length of x and sin y0ACB16Y0X34 x 4 = x 4 = 12 12= 20Sin y0 = Bertentangan hipotenus

= 12 = 3 20 5 5X 4 = 20AIRIL BIN AHMADWednesday, July 29, 2015 trigonometri

Exercise 1ABC is a right angle triangle. Given that tan y0 = 5 / 12, find the length of x and sin y0ACB24Y0XX = 26Sin y0 = Bertentangan hipotenus

= 10 = 5 26 13

AIRIL BIN AHMADWednesday, July 29, 2015 trigonometri

Exercise 2ABC is a right angle triangle. Given that tan y0 = 4 / 3, find the length of x and sin y0ACB24Y0XX = 40Sin y0 = Bertentangan hipotenus

= 18 = 3 30 5

AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise 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 = 8/17cos y = 15/17 Tan y = 8/15

x

AIRIL BIN AHMADWednesday, July 29, 2015 trigonometri

AIRIL BIN AHMADWednesday, July 29, 2015Wednesday, July 29, 2015trigonometri EXERCISEBYAIRIL BIN AHMAD

AIRIL BIN AHMADAIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise 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 = 8/17cos y = 15/17 Tan y = 8/15

x

AIRIL BIN AHMADWednesday, July 29, 2015In the diagram, S is the midpoint of PQ. If tan x = and PR = 10 cm, then tan y =

QUESTION NO.1AIRIL BIN AHMADWednesday, July 29, 2015

QUESTION NO.2In the diagram, EFG and GHI are straight lines.If tan x = 2, then tan y =AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.3

In the diagram, sin x = . The value of y isAIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.4

In the diagram, find the value of sin . AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.5In the diagram, sin t =

. Find the value of x.

AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.6In the diagram, the value of cos x is

2425AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.7

In the diagram, LMN and PNQ are straight lines. If cos x = ,then find tan y. AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.8

In the diagram, tan x = , find value of cos y.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION 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 AHMADWednesday, July 29, 2015QUESTION 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 of t. AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.11

The diagram shows a flagpole that is supported by a wire QR. Find the angle of PRQ, in degree.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.12

In the diagram, KLM is a straight line.Given that tan x = and sin y = Calculate the length, in cm, of LM.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.13

In the diagram, GMH and MFN are straight lines. If sin x = then find the value of tan y.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.14

The diagram shows a rectangle PQRS. M is the midpoint of RS. Find the value of cos x. AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.15

In the diagram, JMK is a straight line. Given that sin x = . Find the value of tan y.AIRIL BIN AHMADWednesday, July 29, 2015

QUESTION NO.16

In the diagram, M is the midpoint of QR.Given that cos y = find the value of tan x.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.17

In the diagram, HJK and JML are straight lines. Find the value of cos y.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.18

In the diagram, find the value oftan B and cos B.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.19

In the diagram, FJMP is a rectangle. JKS and PKM are straight lines. If tan x = then find the value of sin y.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.20

In the diagram, PMR is a straight line. M is the midpoint of PR. Find the value of tan D0.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.21

In the diagram, HJM and JPT are straight lines. Given that cos x = , find the value of tan y o.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.22

Based on the diagram, cos x = , find FG.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.23

In 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 AHMADWednesday, July 29, 2015QUESTION NO.24

In the diagram, PST and QTR are straight lines. S is the midpoint of PT. Given that tan y = find the length of PQ.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.25

The diagram shows a square HJQS. Find the value of sin x.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.26

In the diagram, PQR is a straight line. If sin x = , then find the value of tan y. AIRIL BIN AHMADWednesday, July 29, 2015

QUESTION NO.27In the diagram, JPK is a straight line. Given that JP = 7 cm, calculate the value of tan x.AIRIL BIN AHMADWednesday, July 29, 2015

30cmQUESTION NO.28

In the diagram, PQR is a straight line. Given that sin x = . Find the length of PR.AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.29

BMCA x50 cm

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 AHMADWednesday, July 29, 2015

7 m24 mxQUESTION 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 AHMADWednesday, July 29, 2015Wednesday, July 29, 2015

AIRIL BIN AHMADWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015trigonometri(Using Calculator)BYAIRIL BIN AHMAD

AIRIL BIN AHMADWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometri1 degree (10) = 60 min (600) 10=60Example 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 30.82. Press 0,,,3. Press =

The value obtained is 300 48

= 150 18= 280 30= 500 54

Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise

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

Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 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 302. Press 0,,,3. Press 184. Press 0,,,5. Press =6. Press 0,,,The value obtained is 30.3

= 36.6= 67.9= 62.85

Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise

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


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

a. Sin 300b. Sin 360 36c. Cos 670d. Cos 620 51e. Tan 350 f. Tan 740 20

On your calculator

1. Press sin2. Press 303. Press 0,,,4. Press =

The value obtained is 0.5

= 0.60= 0.39= 0.46

= 0.70= 3.57Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise

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


Using calculator to find the value of the angle

a. Sin = 0.5925b. Cos = 0.5925 c. Tan = 0.9342 d. Sin = 0.2479 e. Sin = 0.7992 f. Cos = 0.3345

On your calculator

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

The value obtained is 36.33460

5. Press 0

The value is 360 20= 530 39= 430 03= 140 21

= 530 03= 700 27Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExerciseFind the value of:a. Sin = 0.8025b. 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 = 0.4425i. Cos = 0.5925 j. Tan = 2.9342 k. Sin = 0.5579 l. Sin = 0.0009 m. Cos = 0.7945


Find the angle of y0

6cmACBY010cmSolution

Sin y0 = Bertentangan hipotenus

sin y0 = 6 = 0.6 10

y = 360 52#Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 6

Find the angle of y0

9cmACBY015cmSolution

Cos y0 = Bersebelahan hipotenus

cos y0 = 9 = 0.6 15

y = 530 07#Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise

1. Find the angle of y0

Exercise

2. Find the angle of y0A5cmCBY08cm7cmACBY011cmWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise


Exercise

4. Find the angle of y04cmACBY09cm3cmACBY07cmWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise


Exercise

6. Find the angle of y06cmACBY013cm8cmACBY011cmWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 7

Find the length of x

XACB3007cmSolution

Sin 300 = Bertentangan hipotenus

sin 300 = x 7 0.5 = x 7 x = 0.5 x 7 x = 3.5cmWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExample 8

Find the length of x

XACB350 276cmSolution

Sin 350 27 = Bertentangan hipotenus

sin 350 27 = x 6 0.5800 = x 6 x = 0.5800 x 6 x = 3.48cmWednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise

1. Find the length of x

Exercise

2. Find the length of xAxCB60012cmxACB5804515cmX=10.39X=12.82Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise


Exercise

4. Find the length of xxACB270197cmxACB6102313cmX=6.22X=6.23Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015 trigonometriExercise


Exercise

6. Find the length of xxACB5205013cmxACB480258cmX=17.15X=9.02Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015QUESTION 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 7Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015QUESTION 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 of t. Question 8Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 2015QUESTION NO.11

The diagram shows a flagpole that is supported by a wire QR. Find the angle of PRQ, in degree. Question 9Wednesday, July 29, 2015AIRIL BIN AHMADWednesday, July 29, 201510. 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.

10m650120m240Wednesday, July 29, 2015AIRIL BIN AHMAD

bengkel trigo 29 julai 2015

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