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ELTC 103
Overview of math topics
The Metric System & Trigonometry
Metric System
• Prefixes for SI units
Multiple
Power of 10 Prefix
Symbol
Meaning
1,000,000,000,000
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
Pico (p)
Trillionth
0.000000000001 10-12
Metric System
• Examples
• Convert 0.00007 F to pF
• Convert 16 4F 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.