Trigonometry Review

61

11cos b

13

12cos a

13

5sin a

222 CBA

61

60sin b

12

5tan a

11

60tan b

5

12a

222 125 C2169 C

13C

13 11

60

b 61

222 CBA 222 6011 C

23721 C

61C

Trigonometry Review

25

24cos d

41

9cos c

41

40sin c

222 CBA

25

7sin d

9

40tan c

24

7tan d

41

40

c

222 4140 B281 B

9B

925 24

d

7

222 CBA 222 2524 A

492 A7A

Trigonometry Review

xa

x =65sin a =3/5cos a =4/5y = ?

r

xa cos

r

65

5

4

3254 r

yr

25.81r

r

ya sin

25.815

3 y

75.48y

xa

tan a =3/4y = 9r = ?

x

ya tan

x

9

4

3

363 x

yr

12x

F=62N

Vector Review

60o

F=48N

30o F=52N

45o

60cos62cos FFx

331yF

jFiFF yx

NjNiF 33131

NFx 3160sin62sin FFy

30cos48cos FFx

24yF

jFiFF yx

NjNiF 24324

324xF

30sin48sin FFy

cosFFx

226yF

jFiFF yx

NjNiF 226226

226xF

sinFFy

Vector Review

ftlbdFW 5.211

s

lbftP

5.27

A swimmer pulls her hands through the water with a force of 11 pounds. Her stroke lasts a distance of 2.5 feet and takes 1 second. How much work does she do with each stroke?

lbftW 5.27

What power is used?

t

WP

Using the efficiency equation, what would the output force be if her stroke were only 60% efficient

F

FEff x

lbs

Fx11

6.0 lbsFx 6.6

jiF 02

jiF 1526

A teacher pushes a television cart 1/8 mile (1 mile = 5,280 feet) down a hall. The television weighs 35 lbs, the cart itself weighs 30 lbs, and friction at the wheels opposes motion with a force of 2 lbs. The teacher pushes the cart at an angle of 30o downward from the horizontal. Write each of the forces acting on the cart in rectangular components. What is the resultant force acting on the cart?

jiF 650

jFiFF 30sin30cos

65lbs30o2lbs

30lbs

Friction

Gravity

Teacher

jlbsilbsFres 8024 Resultant

How much does the force of gravity do to the cart?

Distance =0 in the y directionWork = 0

How much work does the teacher do?

%7.86867. orF

FEff x

lbftftlbW 1720066026How efficiently is pushing the cart?

He pushes in 2 min, how much power is he using?

s

lbft

s

lbft

t

WP

143

120

17200

A radio antenna tower stands 200 meters tall. A supporting cable attached to the top of the tower stretches to the ground and makes a 30o angle with the tower. How far is it from the base of the tower to the cable on the ground?

200m

30o

mm

x 34630tan

200

x

y30tan

How long must the cable be?

r

m20030sin

mr 400

During a storm, the wind blows against the side of the tower with a force with 300 N. The horizontal strength of the cable maintains equilibrium, what is the total force?

200m

30o

jFiFFcable 30sin30cos

jNiFwind 0300

The horizontal component of resultant is 0

030030cos cableF

NN

Fcable 34630cos

300

300N

Trigonometry and VectorsCommon triangles in Geometry and

Trigonometry

11

1

2

45o

45o

2

3

30o

60o

You must memorize these triangles

2 3

IOT

POLY ENGINEERING3-8

Trigonometry and Vectors

SOH CAH TOA

Trigonometric Functions

tan A = opposite adjacent

sin A = opposite

hypotenuse

cos A = adjacent

hypotenuse

IOT

POLY ENGINEERING3-9

Trigonometry and Vectors

3. Free-body DiagramA diagram that shows all external forces acting on an object.

Vectors

friction force

force of gravity

(weight)

applied force

normal force

Wt

FN

Ff

IOT

POLY ENGINEERING3-10

Trigonometry and Vectors

Vectors – Rectangular Components

y

x

F Fx +

Fy +

When are Fx and Fy Positive/Negative?

FFx -

Fy +

FFFx -Fy -

Fx +Fy -

IOT

POLY ENGINEERING3-13

Work

You are pulling a wagon with a 20 lbs of force at a 60o angle. You pull the wagon 10 feet, how much work did you do?

20 lbs

60oFy

Fx

lbsFFx 102

12060cos

lbsftftlbsdFWork x 1001010

IOT

POLY ENGINEERING3-13

Efficiency

You are pulling a wagon with a 20 lbs of force at a 60o angle. How efficiently are you using your pulling

20 lbs

60oFy

Fx

lbsFFx 102

12060cos

%505.020

10or

lbs

lbsEfficiency

IOT

POLY ENGINEERING3-13

Work

You are pulling a wagon with a 20 lbs of force at a 60o angle. You pull the wagon 10 feet in 10 seconds, how much power did you use?

20 lbs

60oFy

Fx lbsFFx 102

12060cos

s

lbsft

s

lbsft

time

WorkPower

10

10

100