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

2. Metric System Prefixes for SI units MultiplePower of 10PrefixSymbolMeaning 1,000,000,000,00010 12 TeraTTrillion 1,000,000,00010 9 GigaGBillion 1,000,00010 6 MegaMMillion 1,00010 3 KilokThousand 10010 2 HectohHundred 1010 1 DekadaTen.110 -1 DecidTenth.0110 -2 CenticHundredth.00110 -3 MillimThousandth.00000110 -6 Micro  Millionth.00000000110 -9 NanonBillionth.00000000000110 -12 PicopTrillionth

3. Metric System Common units in electronics MultiplePower of 10Prefix (symbol) Meaning 0.00000110 -6 Micro (  ) Millionth 0.00000000110 -9 Nano (n)Billionth 0.00000000000110 -12 Pico (p)Trillionth

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) c 2 = a 2 + b 2

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.