ELTC 103

Overview of math topics

The Metric System & Trigonometry

Metric System• Prefixes for SI units

Multiple Power of 10 Prefix Symbol Meaning1,000,000,000,000 1012 Tera T Trillion

1,000,000,000 109 Giga G Billion

1,000,000 106 Mega M Million

1,000 103 Kilo k Thousand

100 102 Hecto h Hundred

10 101 Deka da Ten

.1 10-1 Deci d Tenth

.01 10-2 Centi c Hundredth

.001 10-3 Milli m Thousandth

.000001 10-6 Micro Millionth

.000000001 10-9 Nano n Billionth

.000000000001 10-12 Pico p Trillionth

Metric System

• Common units in electronics

Multiple Power of 10 Prefix (symbol)

Meaning

0.000001 10-6 Micro () Millionth

0.000000001 10-9 Nano (n) Billionth

0.000000000001 10-12 Pico (p) Trillionth

Metric System

• Examples

• Convert 0.00007 F to pF

• Convert 16 4F to nF and pF

Trigonometry

• Types of angles– Obtuse

• Greater than 90°

– Acute• Less than 90°

– Right• Exactly 90°

Trigonometry

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

Trigonometry

• Ex: Find c in the diagram below

Trigonometry

• Ex: Find a in the diagram below

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

Trigonometry

• Ex: Find the 6 trigonometric ratios for A

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

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

Trigonometry

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

Trigonometry

• Ex: Completely solve the given triangle.

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.

Trigonometry

• Example– If the resistance is 55 and the inductive

reactance is 27, find the impedance and the phase angle

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.

Trigonometry

• Example– If the impedance is 70 and = 35°, find the

resistance and the capacitive reactance.