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Math Review

Math Review. Egr 102-2101. Trigonometry. Consider a right triangle as shown with sides a and b and hypotenuse c. B c a A b.

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Math Review

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  1. Math Review Egr 102-2101

  2. Trigonometry • Consider a right triangle as shown with sides a and b and hypotenuse c. • B • c • a • A • b

  3. Angle A is complementary to angle B • A + B = 90⁰ • a2 + b2 = c2 --- Pythagorean Theorem • Sin A = a/c (opposite side/hypotenuse) • Cos A = b/c (adjacent side/hypotenuse) • Tan A = a/b (opposite side/adjacent side) • Sin2 A + cos2A = 1 [Prove this!]

  4. Sin2 A + cos2A = (a/c)2 + (b/c)2 = • (a2 + b2)/c2 = 1 • By the Pythagorean Theorem

  5. Sin A = cos B • Sin A = a/c • Cos B = a/c • So Sin A = cos B if A and B are complementary angles.

  6. Sin 0 = 0 Cos 0 = 1 • Sin 90 = 1 Cos 90 = 0 • Sin 180 = 0 Cos 180 = -1 • Sin 270 = -1 Cos 270 = 0 • Sin 360 = 0 Cos 360 = 1 • Sin and Cos vary in a sinusoidal manner but are out of phase with one another by 90 degrees.

  7. c • a • A b • If the value of c = 2.0 and angle A is 30⁰, • Then a = c sin 30 = 2.0 sin 30 = 2.0 x 0.5 = 1.0 • Then b = c cos 30 = 2.0 x 0.866 = 1.732 • And this checks out by the Pythagorean Theorem

  8. Exponentials • a1 = a • a2 = a x a • a3 = a x a x a • a1 x a2 = a(1+2) = a3 • a1 / a2 = a(1-2) = a-1= 1/a • 53 x 54 = ? • 53 / 54 = ?

  9. 53 x 54 = 57 • 53 / 54 = 5-1

  10. Logarithms • There are basically two types of logarithms we use: • Common logarithms or logs to the base 10 • Natural logarithms or logs to the base e • Common logs are called log • Natural logs are called ln

  11. Working with Logs • Log ab = log a + log b • Log a/b = log a – log b • Log an = n log a • Log a(1/n) = (1/n) log a

  12. log (2)(3) = log 6 = 0.7782 • log 2 = 0.3010 • log 3 = 0.4771 • log 2 + log 3 = 0.7781 • log (2/3) = log (0.667) = -0.1759 • log 2 – log 3 = 0.3010 – 0.4771 = -0.1761 • rounding off errors

  13. log 23 = 3 log 2 = 3(0.3010) = 0.9030 • log 8 = 0.9031 • log 8(1/3) = log 2 • (1/3)log 8 = (1/3)(0.9031) = 0.3010

  14. Exponentials • e-ax = 1/eax • ln (e-ax) = -ax

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