Trigonometry Chapter Playlist

(1)

Trigonometry Chapter

(2)

Trigonometry

(3)

(4)

Surveying

Measure inaccessible distances

70 ft

(5)

Bolt Circles

Trailer Hub

Micro Sprint Quick Change Sprocket Hub

(6)

Piston Travel

290

290 



(7)



290

3.5”

Co

n

ro

d

=

4. 0”



70

Approaching top dead center (70 away).

1.

75 ”



Co

n

ro

d

=

4 .0

”

At top dead center.

5.

75 ”

1.75”

(8)

(9)

Preview of Trig…



Handout



Ruler



Protractor

(10)

84 mm

130 mm

155 mm

S

c t

(11)

84 mm

130 mm

155 mm

RATIO

=

0.5

42

Angle sine cosine tangent

31 0.515 0.857 0.601

32 0.530 0.848 0.625

33 0.545 0.839 0.649

34 0.559 0.829 0.675

35 0.574 0.819 0.700

(12)

84 mm

130 mm

155 mm

RATIO

=

0.8

39

31 0.515 0.857 0.601

32 0.530 0.848 0.625

33 0.545 0.839 0.649

34 0.559 0.829 0.675

35 0.574 0.819 0.700

(13)

84 mm

130 mm

155 mm

RATIO

=

0.6

46

31 0.515 0.857 0.601

32 0.530 0.848 0.625

33 0.545 0.839 0.649

34 0.559 0.829 0.675

35 0.574 0.819 0.700

(14)

16

166 mm

27 °

?

(15)

166 mm

27 °

27 0.454 0.891 0.510

0.454 ?

166 =

(16)

166 mm

27 °

27 0.454 0.891 0.510

0.891 ?

166 =

?

(17)

Trigonometry Section 2

(18)

(19)

Naming the Sides of a Right

Triangle

hypotenuse leg

(20)

Naming the Sides of a Right

Triangle

Names of the Sides

•hypotenuse •opposite •adjacent

A

(21)

Naming the Sides of a Right

Triangle

A

hypotenuse

(22)

Naming the Sides of a Right

Triangle

B

hypotenuse

(23)

Naming the Sides of a Right

Triangle

A _hypotenuse

(24)

Practice Set 2



Page 11

(25)

Trigonometry Section 2

(26)



Use trig ratios to solve problems



sine

ratio



cosine

ratio



tangent

ratio

A

Trigonometry Ratios

A

hypotenuse

opposite

sin A =

hypotenuse

adjacent

cos A =

adjacent

opposite

(27)

Practice



Trig Worksheet #1

“Trig Ratios”



Ruler (mm)



Protractor



Practice Set 3

_{page 16}



#3, 4 only

(28)

50 mm 87 mm 100 mm

50

100 0.5 87

100 0.87 50

87 0.575

28 0.469 0.883 0.532

29 0.485 0.875 0.554

30 0.500 0.866 0.577

31 0.515 0.857 0.601

32 0.530 0.848 0.625

30°

opposite hypote

nuse

(29)

31 mm 24 mm 39 mm

3 1

39

0.795

24

39

0.61

5

3 1

24

1.29

2 52°

48 0.743 0.669 1.111

49 0.755 0.656 1.150

50 0.766 0.643 1.192

51 0.777 0.629 1.235

52 0.788 0.616 1.280

53 0.799 0.602 1.327

54 0.809 0.588 1.376

opposite

hypo tenu

se

(30)

38 mm 117 mm 123 mm

3 8

123

0.309

11 7

123

0.95 ₁

3

8

18°

117

0.32

5

16 0.276 0.961 0.287

17 0.292 0.956 0.306

18 0.309 0.951 0.325

19 0.326 0.946 0.344

20 0.342 0.940 0.364

opposite hypotenu

se

(31)

Calculator Skills

(32)

Calculator

0 0.000 1.000 0.000

2 0.035 0.999 0.035

4 0.070 0.998 0.070

6 0.105 0.995 0.105

8 0.139 0.990 0.141

10 0.174 0.985 0.176

12 0.208 0.978 0.213

14 0.242 0.970 0.249

16 0.276 0.961 0.287

18 0.309 0.951 0.325

20 0.342 0.940 0.364

22 0.375 0.927 0.404

24 0.407 0.914 0.445

26 0.438 0.899 0.488

28 0.469 0.883 0.532

(33)

Check Your Calculator

D

DEG

The calculator display

must show either:

D

or

(34)

CALCULATOR

(35)

Angle

sine

cosine

tangent

31

0.515

0.857

0.601

32

0.530

0.848

0.625

33

0.545

0.839

0.649

34

0.559

0.829

0.675

35

0.574

0.819

0.700

36

0.588

0.809

0.727

37

0.602

0.799

0.754

38

0.616

0.788

0.781

39

0.629

0.777

0.810

40

0.643

0.766

0.839

sine of 35 =

0.574

sin35 =

sin 3 5 =

0.573576436 sin

3 5

(36)

Angle

sine

cosine

tangent

31

0.515

0.857

0.601

32

0.530

0.848

0.625

33

0.545

0.839

0.649

34

0.559

0.829

0.675

35

0.574

0.819

0.700

36

0.588

0.809

0.727

37

0.602

0.799

0.754

38

0.616

0.788

0.781

39

0.629

0.777

0.810

40

0.643

0.766

0.839

tangent of 40 =

0.839

tan40 =

tan 4 0 =

0.839099631 tan

4 0

(37)

CALCULATOR

(38)

Angle

sine

cosine

tangent

61

0.875

0.485

1.804

62

0.883

0.469

1.881

63

0.891

0.454

1.963

64

0.899

0.438

2.050

65

0.906

0.423

2.145

66

0.914

0.407

2.246

67

0.921

0.391

2.356

68

0.927

0.375

2.475

69

0.934

0.358

2.605

70

0.940

0.342

2.747

What angle has a cosine ratio of 0.423?

65 

cos A = 0.423

64.97586456

cos . 4 =

2nd . 4 2 3 2nd2 3 cos

cos-1_0.423

(39)

Angle

sine

cosine

tangent

61

0.875

0.485

1.804

62

0.883

0.469

1.881

63

0.891

0.454

1.963

64

0.899

0.438

2.050

65

0.906

0.423

2.145

66

0.914

0.407

2.246

67

0.921

0.391

2.356

68

0.927

0.375

2.475

69

0.934

0.358

2.605

70

0.940

0.342

2.747

What angle has a sine ratio of 0.940?

70 

sin A = 0.940

70.05155641

sin . 9 =

2nd. 9 4 0 2nd4 0sin

sin-1_0.940

(40)

Practice



Trig Worksheet #2

“Calculator Skills”



Problems 1-3

(41)

Calculator Skills

Review of Basics

(42)

Review of Skills

Determine the Trig Ratio



sin42



= _____



cos10



= ______



tan85



= ______

0.6691

0.9848

11.4301

42 sin

sin 42 = or

10 cos

cos 10 = or

Angle sine cosine tangent

31 0.515 0.857 0.601

32 0.530 0.848 0.625

33 0.545 0.839 0.649

34 0.559 0.829 0.675

35 0.574 0.819 0.700

(43)

Review of Skills

Determine the Angle from a Ratio



sin

A

= 0.9063



Angle

A

= _______



cos

B

= 0.866



Angle

B

= _______



tan

A

= 1.1918



Angle

A

= _______

65 

30 

50 

2nd sin .9063 = .9063 2nd sin

or

Angle sine cosine tangent

31 0.515 0.857 0.601

32 0.530 0.848 0.625

33 0.545 0.839 0.649

34 0.559 0.829 0.675

35 0.574 0.819 0.700

(44)

Calculator Skills Part II

Evaluate Trig Formulas

(45)

Three Possibilities…

opp _hyp

adj A

4”

7”

32

x 12 ft

opp hyp

adj

29

x

9.5”

opp

hyp

adj

tan A= 4”

(46)

cos 29

Three Trig Setups

How to Solve…

opp _hyp

adj A

4”

7”

32

x 12 ft

opp hyp adj 29 x 9.5” opp hyp adj

A = 29.7

tan A= 4” 7”

tan A= 0.5714

A = tan-1(0.5714)

sin 32= x 12 ft

(12 ft)(0.5299) = x

(12 ft) (12 ft)

6.4 ft = x

cos 29= 9.5” _x (x) (x)

cos 29= 9.5” (x)

cos 29

x = 9.5” cos 29

x = 10.9”

cos 29° =

9.5 _x

x

= 10.9”

Calculator Skills Worksheet

#4, Row C

#4, Row D

(47)

Practice



Trig Worksheet #2

“Calculator Skills”

(48)

Trigonometry - Section 2

Solving Right Triangles using Trig

(49)

Memory Device

SOH CAH TOA

If you decide that using trig is a good idea to solve a

(50)

Memory Device



SOH CAH TOA



S

OH

C

AH

T

OA



S

OH

C

AH

T

OA

sin

e

_co

sin

e

ta

ng

en

t

opp

(51)

Trigonometry - Section 2

Solving Right Triangles using Trig

•

Establish a consistent technique to

(52)

Technique

for Solving Right Triangles with Trig

opp hyp

adj

A

4”

7”

A = 29.7

tan A= 4” 7”

S

OH

C

AH

T

OA

 Worksheet 3

 Rehearse the five steps to solve a trig problem.  Goal – Determine the measure of an angle.  You will need – Ruler, protractor, calculator.

(53)

opp

adj hyp

24 mm

71 mm

SOH CAH TOA

24 71

A =

(54)

Technique

for Solving Right Triangles with Trig 32 x 12 ft opp hyp adj 29  x 9.5” opp hyp adj

sin 32= x 12 ft

(12 ft)(0.5299) = x

6.4 ft = x

9.5” cos 29

x = 10.9” SOH CAH TOA _S_OH_C_AH_T_OA

x =

 Worksheet 4

 Rehearse the five steps used to solve a trig

problem.

 Goal – Use trig to determine the length of a

specified side.

 You will need – Ruler, protractor, calculator.

sin A= opp

(55)

31°

opp

adj

hyp SOH CAH TOA

99

31 tan





x

59.5 adj

opp

A



(56)

Additional Practice

