1. UNIT 3 – ENERGY AND POWER 3-8 UNIT 3 Topics Covered
IOT POLY ENGINEERING
3-8
UNIT 3 – ENERGY AND POWER
UNIT 3
Topics Covered
Energy Sources – Fuels and Power Plants
Trigonometry and Vectors
Classical Mechanics:
Force, Work, Energy, and Power
Impacts of Current Generation and Use

2. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry and Vectors
Background – Trigonometry
Trigonometry, triangle measure, from Greek.
Mathematics that deals with the sides and angles of triangles, and their relationships.
Computational Geometry (Geometry – earth measure).
Deals mostly with right triangles.
Historically developed for astronomy and geography.
Not the work of any one person or nation – spans 1000s yrs.
REQUIRED for the study of Calculus.
Currently used mainly in physics, engineering, and chemistry, with applications in natural and social sciences.

3. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry
Total degrees in a triangle:
Three angles of the triangle below:
Three sides of the triangle below:
Pythagorean Theorem:
a2 + b2 = c2
180
A, B, and C
a, b, and c B c a
HYPOTENUSE A C b

4. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry and Vectors
Trigonometry
State the Pythagorean Theorem in words:
“The sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.”
Pythagorean Theorem:
a2 + b2 = c2 B c a
HYPOTENUSE A C b

5. Trigonometry and Vectors
Trigonometry – Pyth. Thm. Problems
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
Solve for the unknown hypotenuse of the following triangles: c) a) b) ? ? ? 3 1 1 4 1
Align equal signs when possible

6. Trigonometry and Vectors
Common triangles in Geometry and Trigonometry 5 3 4 1

7. Trigonometry and Vectors You must memorize these triangles
Common triangles in Geometry and Trigonometry
You must memorize these triangles
45o
60o 2 1 1
30o
45o 1 2 3

8. Trigonometry and Vectors
Trigonometry – Pyth. Thm. Problems
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
Solve for the unknown side of the following triangles: a) b) 13 c) 10 12 ? ? 8 12 15 ?
Divide all sides by triangle
Divide all sides by triangle

9. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry and Vectors
Trigonometric Functions – Sine
Standard triangle labeling.
Sine of <A is equal to the side opposite <A divided by the hypotenuse.
sin A =
opposite hypotenuse B
sin A = ac
OPPOSITE c
HYPOTENUSE a
ADJACENT A C b

10. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry and Vectors
Trigonometric Functions – Cosine
Standard triangle labeling.
Cosine of <A is equal to the side adjacent <A divided by the hypotenuse.
cos A =
adjacent hypotenuse B
cos A = bc
OPPOSITE c
HYPOTENUSE a
ADJACENT A C b

11. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometry and Vectors
Trigonometric Functions – Tangent
Standard triangle labeling.
Tangent of <A is equal to the side opposite <A divided by the side adjacent <A.
tan A =
opposite adjacent B
tan A = ab
OPPOSITE c
HYPOTENUSE a
ADJACENT A C b

12. Trigonometry and Vectors
Trigonometric Function Problems
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
For <A below calculate Sine, Cosine, and Tangent: b) B c) a) 3 4 5 B B 1 1 2
Sketch and answer in your notebook A A C A C C
opp. hyp.
opp. adj.
adj. hyp.
sin A =
tan A =
cos A =

13. Trigonometry and Vectors
Trigonometric Function Problems
For <A below, calculate Sine, Cosine, and Tangent: 3 4 5 B
sin A =
opposite hypotenuse a) 35
opposite adjacent
sin A =
tan A = A C 34
cos A =
adjacent hypotenuse
tan A = 45
cos A =

14. Trigonometry and Vectors
Trigonometric Function Problems
For <A below, calculate Sine, Cosine, and Tangent: B
sin A =
opposite hypotenuse 1 b)
1 √2
opposite adjacent
sin A =
tan A = A C
cos A =
adjacent hypotenuse
tan A = 1
1 √2
cos A =

15. Trigonometry and Vectors
Trigonometric Function Problems
For <A below, calculate Sine, Cosine, and Tangent:
sin A =
opposite hypotenuse B c) 1 2
1 2
opposite adjacent
sin A =
tan A = A C
1 √3
cos A =
adjacent hypotenuse
tan A =
√3 2
cos A =

16. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometric Functions
Trigonometric functions are ratios of the lengths of the segments that make up angles.
sin A =
opposite hypotenuse
cos A =
adjacent hypotenuse
tan A =
opposite adjacent

17. Trigonometry and Vectors You must memorize these triangles
Common triangles in Trigonometry
You must memorize these triangles 1
45o 1 2
30o
60o

18. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometric Functions
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
Calculate sine, cosine, and tangent for the following angles:
30o
60o
45o 12
sin 30 = 1 2
30o
60o
√3 2
cos 30 =
1 √3
tan 30 =

19. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometric Functions
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
Calculate sine, cosine, and tangent for the following angles:
30o
60o
45o
√3 2
sin 60 = 1 2
30o
60o 12
cos 60 =
tan 60 = √3

20. Trigonometry and Vectors
IOT POLY ENGINEERING
3-8
Trigonometric Functions
NO CALCULATORS – SKETCH – SIMPLIFY ANSWERS
Calculate sine, cosine, and tangent for the following angles:
30o
60o
45o 1
45o
1 √2
cos 45 =
1 √2
sin 45 =
tan 45 = 1

21. Trigonometry and Vectors
Measuring Angles
Unless otherwise specified:
Positive angles measured counter-clockwise from the horizontal.
Negative angles measured clockwise from the horizontal.
We call the horizontal line 0o, or the initial side 90
30 degrees
45 degrees
90 degrees
180 degrees
270 degrees
360 degrees =
-330 degrees
-315 degrees
-270 degrees
-180 degrees
-90 degrees
180
INITIAL SIDE
IOT POLY ENGINEERING
3-8
270

22. Trigonometry and Vectors
Begin all lines as light construction lines!
Draw the initial side – horizontal line.
From each vertex, precisely measure the angle with a protractor.
Measure 1” along the hypotenuse. Using protractor, draw vertical line from the 1” point.
Darken the triangle.

23. Trigonometry and Vectors
CLASSWORK / HOMEWORK
Complete problems 1-3 on the Trigonometry Worksheet