Trigonometry Chapter Playlist

(1)

Trigonometry Chapter

(2)

Trigonometry

(3)

(4)

Surveying

Measure inaccessible distances

distance

(5)

Surveying

x

70 ft

37°

x

= 52.7 ft across tan37°=

x

70 ft

opp.

(6)

Surveying

70 ft

37°

(7)

Crime Scene Investigation

■

Trigonometric Shooting Reconstruction

Method

■

MySWTC

College Math

Course

(8)

Inside of wall

floor

Crime Scene Investigation

Horizontal impact angleα

α

(9)

Bolt Circles

Trailer Hub

Micro Sprint Quick Change Sprocket Hub

(10)

Bolt Circle

+ +

+

x

radius 2.4” _2.4”

2.4”

(11)

Piston Travel

290°

(12)

∙

290°

3.5”

Con rod = 4.0”

∙

70°

Approaching top dead center (70° away).

1.75”

∙

Con rod = 4.0”

At top dead center.

5.75”

1.75”

(13)

(14)

Blueprints

23 ft 18 ft

? ft

15 ft

30° 30°

(15)

Preview of Trig…

■

Handout

■

Ruler

■

Protractor

(16)

84 mm

130 mm

155 mm

S c t

(17)

84 mm

130 mm

155 mm

RATIO

=

0.542

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

(18)

84 mm

130 mm

155 mm

RATIO

=

0.839

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

(19)

84 mm

130 mm

155 mm

RATIO

=

0.646

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

(20)

16

166 mm

27°

?

(21)

166 mm

27°

27 0.454 0.891 0.510

0.454 ?

166 =

?

(22)

166 mm

27°

27 0.454 0.891 0.510

0.891 ?

166 =

?

(23)

Trigonometry Section 2

(24)

80°

14 ft

30 ft A

40° d

55 mm

20 mm 23 mm

(25)

Trigonometry

■

What information can be

computed?

■

If you know a

■

length

■

and angle…

50°

3.55”

x

(26)

Trigonometry

12.65”

7.75”

x

°

■

What information can be

computed?

■

If you know

■

Two lengths…

(27)

LABELING TRIANGLES

(28)

Naming the Sides of a Right

Triangle

hypotenuse leg

(29)

Naming the Sides of a Right

Triangle

Names of the Sides

•hypotenuse •opposite •adjacent A

(30)

Naming the Sides of a Right

Triangle

•hypotenuse •opposite •adjacent A

hypotenuse

(31)

Naming the Sides of a Right

Triangle

•hypotenuse •opposite •adjacent

B

hypotenuse

(32)

Naming the Sides of a Right

Triangle

A _hypotenuse

(33)

Practice Set 2

■

Page 11

(34)

Trigonometry Section 2

(35)

■

Ratios are

comparisons

between two numbers.

■

Format:

■

4 to 5

4:5

4/5

■

WeedEater:

■

What is the

gas

to

oil

ratio?

■

Mix 2 ounces of oil for every 50 ounces of gas.

Ratios: Review

Gas

Oil

50

2

25

(36)

Write a Ratio

■

State the ratio of

length

to

width

of a

picture frame with the following

dimensions.

L=14”

W=12”

length

width

14

12

(37)

■

Use trig ratios to solve problems

■

sine ratio

■

cosine ratio

■

tangent ratio

A

Trigonometry Ratios

A A

hypotenuse

opposite

sin

A

=

hypotenuse

adjacent

cos

A

=

adjacent

opposite

(38)

Practice

■

Trig Worksheet #1

“Trig Ratios”

■

Ruler (mm)

■

Protractor

■

Practice Set 3

page 16 ■

#3, 4 only

(39)

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

hypotenuse

(40)

31 mm 24 mm 39 mm

31

39

0.795

24

39

0.615

31

24

1.292 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 hypotenuse

(41)

38 mm 117 mm 123 mm

38

123

0.309

117

123

0.951

38

18°

117

0.325

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 hypotenuse

(42)

Ratios in Right Triangles

sin A =

hypotenuse

opposite

A

2.2 in

0.801 in

2.341 in

A

0.801

2.341

opp

adj

hyp

(43)

Ratios in Right Triangles

cos A =

hypotenuse

adjacent

A

2.2 in

0.801 in

2.341 in

A

2.2

2.341

opp

adj

hyp

0.940

(44)

Ratios in Right Triangles

tan A =

adjacent

opposite

A

2.2 in

0.801 in

2.341 in

A

0.801

2.2

opp adj hyp

0.364

(45)

Determine Angle using Ratios

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

30° 0.500 0.866 0.577

There is only one angle between 0

°

and 90

°

that has the following ratios:

sine ratio = 0.342

cosine ratio = 0.940

tangent ratio = 0.364

?

(46)

Calculator Skills

(47)

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

(48)

Check Your Calculator

D

DEG

The calculator display

must show either:

D

or

(49)

CALCULATOR

(50)

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 =

0.57357643 6

sin 3 5

(51)

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 =

0.83909963 1

tan 4 0

(52)

CALCULATOR

(53)

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 _64.9758645

6

cos . 4 =

2nd . 4 2 3 2nd2 3 cos

(54)

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 _70.0515564

1

sin . 9 =

2nd. 9 4 0 2nd4 0sin

(55)

Calculator

0.899 0.438 2.050

sin64° =

° ° °

cos64° =

tan64° =

sin64 °

sin 6 4 = _0.898794046

sin

6 4 _0.898794046 D.A.L.

(56)

Angle

sine

cosine tangent

25°

0.4226

0.9063

0.4663

0.4540

0.8910

0.5095

Calculator

sinA = 0.4540

sin

-1

( sinA) =

sin

-1

(0.4540)

A =

sin

-1

(0.4540)

27°

sin . 4 = _27.00061091

2nd 5 4 0

4

. 5 4 0 2nd sin _27.00061091 D.A.L.

(57)

Practice

■

Trig Worksheet #2

“Calculator Skills”

■

Problems 1-3

(58)

Calculator Skills

Review of Basics

(59)

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

(60)

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

(61)

Calculator Skills Part II

(62)

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”

7” sin 32°= x

12 ft cos 29°=

x

9.5”

(63)

cos 29°

Three Trig Setups

How to Solve…

opp _hyp

adj A

4”

7”

32°

x 12 ft

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°= x

9.5”

(x) (x)

cos 29°= 9.5”

(x)

cos 29°

x = 9.5” cos 29°

x = 10.9”

Angle

Length

cos 29° =

x

9.5 x = 10.9”

Calculator Skills Worksheet #4, Row C

Calculator Skills Worksheet #4, Row D

(64)

Compute Angles

Introduction

A B

C 28”

37”

0.7568 28”

37”

opp

(65)

Solving Trig Formulas

Angles

(66)

x

4

Compute Length

“top number” unknown

■

Determine the length of side

x

.

28° 4”

x

opp

hyp

adj

sin 28° =

(4)

(67)

Solving Trig Formulas

Length of Sides

(68)

Solving Problems

A Function name A = length1

length₂

?

(69)

x

325

Compute Length

“bottom number” unknown

49°

325 mm

x

opp

hyp

adj

sin 49° =

(x)

x = 430.6 mm

(x)sin 49° = 325

sin 49°

x = 325

(70)

cos 29°

Technique

32°

x 12 ft

sin 32°= x 12 ft

(12 ft)(0.5299) = x

6.4 ft = x

cos 29°= x

9.5”

(x) (x)

cos 29°= 9.5”

(x)

cos 29°

x = 9.5” cos 29°

(71)

Solving Trig Formulas

Length of Sides

■

Solve for length x:

cos 38° =

x

365

(72)

Practice

■

Trig Worksheet #2

“Calculator Skills”

(73)

Trigonometry - Section 2

Solving Right Triangles using Trig

(74)

Memory Device

SOH CAH TOA

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

(75)

Memory Device

■

SOH CAH TOA

■

S

OH

C

AH

T

OA

■

S

OH

C

AH

T

OA

sine

_cosine

tangent

opp

hyp

adj

hyp

(76)

Trigonometry - Section 2

Solving Right Triangles using Trig

(77)

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.

(78)

opp

adj hyp

24 mm

71 mm

SOH CAH TOA

24 71

(79)

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

(80)

31°

opp

adj

hyp SOH CAH TOA

(81)

Example 1

Determine angle T

T 3.65”

2.70” 1.) Identify the reference angle.

2.) 4.) 5.) 3.) Label“Shop”Setup Discard the sides.formula and solve for unknown. for a trig formula.unneeded information.