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 5 2 exponent 5 * 5 = = 2 * 2 * 2 = 8 25= 25 1/2 = 5

3 Order of Operations Solve the following problem (12 + * 3) * 2 - (8/4) /2 = ??? 2 3

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

6 Trigonometry Review  c a b a = “opposite” side b = “adjacent” side c = “hypotenuse”  = angle

7 SOHCAHTOA  c a b 4 Basic Relationships 1. a 2 + b 2 = c 2 (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 GivenSolve For c &  a & b a & b c &   c a b

10 TYPE A Problem v = 10 m/s 40 o b a Given: c = 10 m/s  = 40 degrees Find:a and b sin 40 o = a 10 m/s 10 m/s * sin = a 10 m/s 40 o cos 40 o = b 10 m/s 10 m/s * cos = b 10 m/s 40 o b = 10 m/s * cos 40 = 7.66 m/s a = 10 m/s * sin 40 = 6.43 m/s o o

11 Type B Problem 100 lb 400 lb c  Given: a = 400 lb, b = 100 lb Find: c and  a 2 + b 2 = c 2 (400 lb) 2 + (100 lb) 2 = c lb lb 2 = c lb 2 = c 2 c = lb a tan  = b 400 lb tan  = 100 lb tan  = 4 tan -1 (tan  ) = tan -1 (4)  = 76.0 o

12 Inverse Trig Functions If sin is a trig function then sin -1 is an inverse trig function :inverse trig functions simply “undo” trig functions

o b a Calculate the vertical (a) and horizontal sides of this right triangle.

c  Solve for the length of 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)