Now don't you fret or frown, for those whom the word «trig» conjures up feelings of pain, angst, and frustration, have no fear. We will need only the most basic of algebra and trigonometry knowledge in order to successfully solve a wide range of physics problems.
A vast majority of problems requiring algebra can be solved using the same problem solving strategy. First, analyze the problem and write down what you know, what you need to find, and make a picture or diagram to better understand the problem if it makes sense. Then, start your solution by searching for a path that will lead you from your givens to your finds. Once you've determined an appropriate pathway (and there may be more than one), solve your problem algebraically for your answer. Finally, as your last steps, substitute in any values with units into your final equation, and solve for your answer, with units.
Our use of trigonometry, the study of right triangles, can be distilled down to the definitions of the three basic trigonometric functions. When you know the length of two sides of a right triangle, or the length of one side and a non-right angle, you can solve for all the angles and sides of the triangle. If you can use the definitions of the sine, cosine, and tangent, you'll be fine in this course.
Of course, if you need to solve for the angles themselves, you can use the inverse trigonometric functions.
VI. Arrange the expressions using the suitable words in the following two columns
1) to know a) a diagram
2) to understand b) the natural world
3) to determine c) the length of a right triangle
4) to use d) problems
5) a convenient e) behavior
6) need f) an appropriate pathway
7) to study g) knowledge
8) make h) functions
9) to solve i) basic algebra
10) to describe j) tool
VII. Answer the questions on the text
1. For what purpose do we need a special language for conveying our understanding of the world?
2. Why do we have to study basic of algebra and trigonometry?
3. How can the majority of problems requiring algebra be solved?
4. A car travels from the airport 14 miles east and 7 miles north to its destination. What direction should a helicopter fly from the airport to reach the same destination, traveling in a straight line?
UNIT 4
Vocabulary
quantity n. – количество;
to represent v. – 1) представлять; 2) изображать; отражать;
to include v. – включать;
force n. – 1) сила; 2) действие;
velocity n. – скорость;
acceleration n. – ускорение;
concept n. – 1) концепция; 2) понятие;
arrow n. – стрелка;
to indicate v. – указывать; показывать;
magnitude n. – 1) размеры; 2) важность;
space n. – 1) космос; 2) пространство;
to reverse – поменять; поворачивать;
retain n. – 1) покой, отдых; 2) остаток;
resultant n. – сумма двух векторов;
to draw v. – вытягивать, отодвигать, подтягивать, приближать;
I. Practice pronunciation of the following words:
Vector ['vɛktə] velocity [vɪ'lɒsɪti]
Scalar ['skeɪlə] acceleration [əksɛlə'reɪʃ(ə)n]
examine [ɪɡ'zamɪn] concept ['kɒnsɛpt ]
magnitude ['maɡnɪtju: d] arrow ['arəʊ]
quantity ['kwɒntɪti] figure ['fɪɡə]
temperature ['tɛmp(ə)rətʃə] straight [streɪt]
descriptive [dɪ'skrɪptɪv] touch [tʌtʃ]
force [fɔ:s] resultant [rɪ'zʌlt(ə)nt]
II. Read and translate the words having the same root representing – represented – representment – misrepresent; directional – indirection – misdirection– directions; acceleration – accelerated – accelerating; indicated – indication – indicative – indicator; reversal – reversible – reversion – reversed – reverser – reversing.
III. Match the following words (a, b, c…) with the statements (1, 2, 3…)
a) confuse
b) concept c
) to represent
d) magnitude
e) arrow
f) to line up
g) to retain
h) acceleration
1) the sign that shows where something is or where you should go
2) difficult to understand
3) to be an example or sign of something
4) to stay without changes
5) the size, extent, or importance of something
6) physical term, representing decreasing or increasing velocity by time
7) to stand in a line or make a line
8) picture in your mind
IV. Insert prepositions: of, into, on, to, at
1. Mechanical engineering achieved a prominent position _______ the very beginning.
2. Energy can change from one type ________another.
3. Electrical