1

Mathematical Fundamentals

• Need working knowledge of algebra and basic trigonometry

• if you don’t have this then you must see me immediately!

2

Algebra Review

• Exponents - Square Roots

52

exponent

5 * 5 = 25

23 = 2 * 2 * 2 = 8

25 = 251/2

= 5

3

Order of Operations

• Solve the following problem

(12 + * 3)2-1 + 3 * 2 - (8/4) - 52 - 6/2 = ???23

4

5

Trigonometry

• field of mathematics focusing on relationships between sides of and the angles within a right triangle

6

Trigonometry Review

ca

b

a = “opposite” sideb = “adjacent” sidec = “hypotenuse” = angle

7

SOHCAHTOA

ca

b

4 Basic Relationships1. a2 + b2 = c2

(Pythagorean Theorem)

2. sin = opp/hyp = a/c

3. cos = adj/hyp = b/c

4. tan = opp/adj = a/b

a = “vertical component”b = “horizontal component”c = “resultant”

8

SOHCAHTOA

• SOH Sine = Opposite/Hypotenuse

• CAH Cosine = Adjacent/Hypotenuse

• TOA Tangent = Opposite/Adjacent

9

Two types of TRIG problems

Type A

Type B

Given Solve For c & a & b

a & b c &

ca

b

10

TYPE A Problem

v = 10 m

/s

40o

b

aGiven:

c = 10 m/s = 40 degrees

Find: a and b

sin 40o

=a

10 m/s

10 m/s * sin = a

10 m/s10 m/s40

o

cos 40o

=b

10 m/s

10 m/s * cos = b

10 m/s10 m/s40

o

b = 10 m/s * cos 40 = 7.66 m/sa = 10 m/s * sin 40 = 6.43 m/so o

11

Type B Problem

100 lb

400 lbc

Given: a = 400 lb, b = 100 lbFind: c and

a2 + b2 = c2

(400 lb)2 + (100 lb)2 = c2

160000 lb2 + 10000 lb2 = c2

170000 lb2 = c2

c = 412.3 lb

atan = b

400 lbtan= 100 lb

tan= 4

tan-1 (tan ) = tan-1(4)

= 76.0o

12

Inverse Trig Functions

If sin is a trig function

then sin-1 is aninverse trig function

:inverse trig functions simply “undo” trig functions

13

25

20o

b

a

Calculate the vertical (a) and horizontalsides of this right triangle.

14

10

15c

Solve for the lengthof the hypotenuse (c)and the angle, .

15

UNITS

• Use the SI system– AKA Metric System– 4 basic units

• length -- meter• mass -- kilogram• time -- second• temperature -- degree Kelvin

(Celsius)