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EET 109 MathJanuary 14, 2016
Week 2 Day 2
Chapter 1
Fundamental Concepts
1.2 ZERO AND ORDER OF OPERATIONS
1.11 FORMULAS page 42
Solving a formula means to isolate a given letter on one side of the equal sign.
We solve formulas using the same principles used solving equations, not with a calculator.
1.12 SUBSTITUTION OF DATA INTO FORMULAS Page 45
Be careful about reversing numbers 1 and 2.
Exercises 1.12 page 48 number 13
The unit for L is not given and so is not part of the answer.
Inductance is measured in units called henrys.One henry is the amount of inductance necessary to induce one volt when the current in coil changes at a rate of one ampere per second.
Exercises 1.12 page 48 number 13
75.0 is 2 keystrokes on a calculator that do nothing but create an opportunity to make a data entry error.
75Ω is just a unit and is not needed for calculations.
Hz is just a unit and is not needed for calculations.
Rounding456.8923476123.782965
x 543.78933
30,754,271.72
456.9123.8
x 543.8 30,759,622
Rounding456.8923476123.782965
x 543.78933
30,754,271.72 30.75 M somethings
456.9123.8
x 543.8 30,759,622 30.76 M somethings
Rounding456.8923476123.782965
x 543.78933 30.8E6
456.9123.8
x 543.8 30.8E6
1.11 FORMULAS page 42To solve a formula for a given letter means to isolate the given letter on one side of the equation and express it in terms of all the remaining letters
In class proof and white board exercise.
Chapter 3
Right-Triangle Trigonometry
A right triangle has one right angle and two acute angles.
A right angle is an angle of 90°An acute angle is an angle whose measure is less than 90°.
The two acute angles of a right triangle are complementary. That is:
Solve for A.Solve for B.
Once the value of one acute angle is known, we can find the value of the other.
Page 115
Angles can be measured using any of four units of measure:
revolutions degrees
radians minutes/seconds
Degrees 360 degrees = 1 revolution
A minute in trigonometry is 1/60 of a degree.
The symbol is used to ’ denote minutes.
A second is defined to be1/60 of a minute. The symbol
” is used to denote seconds.
1 Minute = 60 Seconds
1 Degree = 60 minutes
Latitude
At 38 degrees North latitude, one degree of latitude equals approximately 69 miles, one minute equals 1.15 milesone-second equals 101 ft
The one radian is just under 57.3 degrees.
2 π radians is a complete circle (one complete revolution).
π = 3.143.14/180 = .01745180/3.14 = 57.295
Where are the triangle?
Graphing Sine page 421
Sine = Op/Hyp
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/complex/cmplx.html
3.2 VALUES OF THE TRIGONOMETRIC RATIOS page 124
An equilateral triangle is a triangle in which all three sides are equal.
A, B, C are angles.a, b, c are sides.
The Pythagorean theorem gives the relationship
among the sides of a right triangle.
Pythagorean Theorem page 118
3.1 THE TRIGONOMETRIC RATIOS page 118
Know the Pythagorean Theorem:
Why Doug?
3.1 THE TRIGONOMETRIC RATIOS page 118
Page 119
The 6 trigonometric ratios express the relationship between an acute angle of a right triangle and the length of 2 sides.
Page 119
Trigonometric ratios express the relationship between an acute angle and the length of 2 sides.
Page 122
Page 133Note: While all six trigonometric rations may be used to solve a right triangle, we will usually choose sine, cosine, and tangent because these buttons appear on calculators.
The Soup is Cold o a oh ah
Tan = Op/AdjSin = Op/HypCos = Adj/Hyp
SOH CAH TOASin = Op/HypCos = Adj/HypTan = Op/Adj
The side opposite the angle.
The side opposite the angle.
Page 122
The corresponding pairs of reciprocals are called reciprocal trigonometric functions.
Know your calculator.
The TAN of 30 degrees is .577TAN = Opposite / Adjacent Opposite / Adjacent
Opposite / Adjacent
30 degrees
In class exercise from 3.2 page 129
Use a calculator to find the value of each rounded to four significant digits.This is calculator input not so much
understanding trigonometery.
cos 17° = sin 55° =
In class exercise from 3.2 page 129
Use a calculator to find each angle rounded to the nearest tenth of a degree.
sin = 0.4305
cos = 0.1463
Page 122
Tangent of 45 degrees = 1
45 degrees = 1
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