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POLY ENGINEERING3-9

DRILL

January __, 2009

Complete #4 on the Trigonometry worksheet. Measure lengths to the nearest 1/16”.

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POLY ENGINEERING3-9

1. Energy Sources – Fuels and Power Plants2. Trigonometry and Vectors3. Classical Mechanics:

Force, Work, Energy, and Power4. Impacts of Current Generation and Use

UNIT 3 – ENERGY AND POWER

Topics Covered

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POLY ENGINEERING3-9

HOMEWORK

sin A = ac cos A =

bc

tan A = ab

45o

30o

45o

30o1 2 3

2

√2

√3 √3

√23 4

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POLY ENGINEERING3-9

HOMEWORK

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POLY ENGINEERING3-9

DRILLComplete #4 on the Trigonometry worksheet.

tan A = opposite adjacentsin A =

opposite hypotenuse cos A =

adjacent hypotenuse

sin = 3/16

tan = ~3/16

sin = 5/16

tan = 1/3

sin = 1/2

tan = 4/7

sin = 5/8

tan = 5/6

sin = 11/16

tan = 1

sin = 3/4

tan = 1 1/5

sin = 7/8

tan = 1 3/4

sin = 1/8

tan = ~1/8

1. Sketch (sketches go on right side)

2. Write formula (and alter if necessary)

3. Substitute and solve (box answers)

4. Check your solution (make sense?)

Trigonometry and VectorsAlgebra Using Trig Functions

5 2a

sin a= y r

sin a= 2 5

x

We will now go over methods for solving #5 and #6 on

Trigonometry Worksheet

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POLY ENGINEERING3-9

Multiply both sides by rr ya

cos a= x r

r (cos a)= x 10Divide both sides by cos a

r = x

cos a Substitute and Solve= 10 2/5

= (10) 5 2

r = 25

25

Use to solve for y

1. Sketch (sketches go on right side)

2. Write formula (and alter if necessary)

3. Substitute and solve (box answers)

4. Check your solution (make sense?)

Algebra Using Trig FunctionsTrigonometry and Vectors

Trigonometry and Vectors

HOMEWORK

1. Complete problems 4-6 on the Trig. Worksheet

[2. Will be covered shortly]

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POLY ENGINEERING3-9

Trigonometry and Vectors

1. Scalar Quantities – a quantity that involves magnitude only; direction is not importantTiger Woods – 6’1”Shaquille O’Neill – 7’0”

2. Vector Quantities – a quantity that involves both magnitude and direction

Vectors

How hard to impact the cue ball is only part of the game – you need to know direction too

Weight is a vector quantity

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POLY ENGINEERING3-9

Trigonometry and Vectors

1. 5 miles northeast

2. 6 yards

3. 1000 lbs force

Scalar or Vector?

VectorMagnitude and Direction

ScalarMagnitude only

ScalarMagnitude only

4. 400 mph due north

5. $100

6. 10 lbs weight

VectorMagnitude and Direction

ScalarMagnitude only

VectorMagnitude and Direction

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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

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POLY ENGINEERING3-9

Trigonometry and Vectors

4. Describing vectors – We MUST represent both magnitude and direction.

Describe the force applied to the wagon by the skeleton:

Vectors

45o40 lb

s

magnitude direction

F = 40 lbs 45o

Hat signifies vector quantity

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POLY ENGINEERING3-9

Trigonometry and Vectors

2 ways of describing vectors…

Vectors

45o40 lb

s

F = 40 lbs 45o

F = 40 lbs @ 45o

Students must use this form

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POLY ENGINEERING3-9

Trigonometry and Vectors

Describe the force needed to shoot the cue ball into each pocket:• Draw a line from center of cue ball to center of pocket. • Measure the length of line: 1” = 1 lb force.• Measure the required angle from the given initial side.

Describing Vectors

32

1

4 65

INITIAL SIDE

X” = Y lbs.

Zo

F = 3 13/16 lbs. < 14o

Answer to #1

Trigonometry and Vectors

CLASSWORK / HOMEWORK

1. Complete problems 4-6 on the Trig. Worksheet

2. Complete problems 1-2 on the Vector Worksheet