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Mathematical Fundamentals

Mathematical Fundamentals. Need working knowledge of algebra and basic trigonometry if you don’t have this then you must see me immediately!. 3. 2. Algebra Review. Exponents - Square Roots. 1/2. 2. 25. = 25. 5. exponent. = 5. 5 * 5 = 25. = 2 * 2 * 2 = 8. 2. 3.

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Mathematical Fundamentals

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  1. Mathematical Fundamentals • Need working knowledge of algebra and basic trigonometry • if you don’t have this then you must see me immediately!

  2. 3 2 Algebra Review • Exponents - Square Roots 1/2 2 25 = 25 5 exponent = 5 5 * 5 = 25 = 2 * 2 * 2 = 8

  3. 2 3 Order of Operations • Solve the following problem (12 + * 3)2-1 + 3 * 2 - (8/4) - 52 - 6/2 = ???

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

  5. c a q b Trigonometry Review a = “opposite” side b = “adjacent” side c = “hypotenuse” q = angle

  6. c a q b SOHCAHTOA 4 Basic Relationships 1. a2 + b2 = c2 (Pythagorean Theorem) 2. sin q = opp/hyp = a/c 3. cos q = adj/hyp = b/c 4. tan q = opp/adj = a/b a = “vertical component” b = “horizontal component” c = “resultant”

  7. SOHCAHTOA • SOH Sine = Opposite/Hypotenuse • CAH Cosine = Adjacent/Hypotenuse • TOA Tangent = Opposite/Adjacent

  8. Two types of TRIG problems Given Solve For c & q a & b a & b c & q Type A Type B c a q b

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

  10. a tan q = b 400 lb tan q = 100 lb Type B Problem Given: a = 400 lb, b = 100 lb Find: c and q c 400 lb q 100 lb a2 + b2 = c2 (400 lb)2 + (100 lb)2 = c2 160000 lb2 + 10000 lb2 = c2 170000 lb2 = c2 c = 412.3 lb tan q = 4 tan-1 (tan q) = tan-1(4) o q = 76.0

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

  12. 25 a o 20 b Calculate the vertical (a) and horizontal sides of this right triangle.

  13. c 15 q 10 Solve for the length of the hypotenuse (c) and the angle, q.

  14. UNITS • Use the SI system • AKA Metric System • 4 basic units • length -- meter • mass -- kilogram • time -- second • temperature -- degree Kelvin (Celsius)

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