Trigonometry Review 5 12 a 13 11 60 b 61. Trigonometry Review 41 40 c 9 25 24 d 7.
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Transcript of Trigonometry Review 5 12 a 13 11 60 b 61. Trigonometry Review 41 40 c 9 25 24 d 7.
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