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ELTC 103

ELTC 103. Overview of math topics The Metric System & Trigonometry. Metric System. Prefixes for SI units. Metric System. Common units in electronics. Metric System. Examples Convert 0.00007 F to pF Convert 16 4 F to nF and pF. Trigonometry. Types of angles Obtuse

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ELTC 103

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  1. ELTC 103 Overview of math topics The Metric System & Trigonometry

  2. Metric System • Prefixes for SI units

  3. Metric System • Common units in electronics

  4. Metric System • Examples • Convert 0.00007 F to pF • Convert 16 4F to nF and pF

  5. Trigonometry • Types of angles • Obtuse • Greater than 90° • Acute • Less than 90° • Right • Exactly 90°

  6. Trigonometry • Pythagorean Theorem (Right triangles) c2 = a2 + b2

  7. Trigonometry • Ex: Find c in the diagram below

  8. Trigonometry • Ex: Find a in the diagram below

  9. Trigonometry • Trigonometric ratios • Relationship between an acute angle of a right triangle and the lengths of its sides • sin A = side opposite A hypotenuse • cos A = side adjacent to A hypotenuse • tan A = side opposite A side adjacent to A • cot A = side adjacent to A side opposite A • sec A = hypotenuse side adjacent to A • csc A = hypotenuse side opposite A

  10. Trigonometry • Ex: Find the 6 trigonometric ratios for A

  11. Trigonometry • Trigonometric ratios of the other angles. • Use a calculator • Examples: • Finding a trig value given the angle • Find sin 65.25° • Finding the angle given the trig value(inverse or arc function) • Find  if cos = 0.5402

  12. Trigonometry • Solving a triangle – Finding unknown values of sides or angles • Tools needed to solve triangles • Pythagorean theorem • Complementary angles add to 90° • Trigonometric ratios

  13. Trigonometry • Ex: Find angle A to the nearest hundredth of a degree.

  14. Trigonometry • Ex: Completely solve the given triangle.

  15. Trigonometry • The impedance of a series circuit containing a resistance and an inductance can be represented as follows. Here  is the phase angle indicating the amount the current lags behind the voltage.

  16. Trigonometry • Example • If the resistance is 55 and the inductive reactance is 27, find the impedance and the phase angle

  17. Trigonometry • The impedance of a series circuit containing a resistance and an capacitance can be represented as follows. Here  is the phase angle indicating the amount the voltage lags behind the current.

  18. Trigonometry • Example • If the impedance is 70 and  = 35°, find the resistance and the capacitive reactance.

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