a. Match the synonyms
1) convenient a) issue
2) tool b) huge
3) function c) significant
4) basic d) ultimate
5) problem e) main
6) vast f) plurality
7) important g) instrument
8) substitute h) comfortable
9) final i) alternative
10) majority j) operation
b. Match the antonyms
1) determine a) stop
2) range b) expand
3) make c) reverse
4) wide d) destroy
5) replace e) unsuitable
6) produce f) dislike
7) reduce g) commence
8) appropriate h) remain
9) require i) narrow
10) inverse j) domain
III. Fill in the gaps with the words below
1. Physicists use ____________to measure things from speed to capacitance.
2. Scientists need a powerful device to _________ a molecule's form and function.
3. The ____________, with sine and tangent, is one of the three most common trigonometric functions.
4. It is not easy to find alternate ways _____________ physics concepts to non-physicists.
5. Scientists believe that nuclear power is necessary to __________the gas power.
IV. Mind the explanation of the following terms algebra – (no plural) a type of mathematics in which letters and symbols are used to represent numbers.
trigonometry – branch of mathematics that studies relationships involving lengths and angles of triangles.
sine – the ratio of the side opposite a given acute angle to the hypotenuse.
cosine – the ratio of the side adjacent to a given angle to the hypotenuse.
tangent – the ratio of the side opposite a given angle to the side adjacent to the angle.
adjacent – lying near, close, or contiguous, adjoining, neighboring.
hypotenuse – the side of a right triangle opposite the right angle.
V. Read and translate the text
Algebra and Trigonometry
Just as we find the English language a convenient tool for conveying thoughts to each other, we need a convenient language for conveying our understanding of the world around us in order to understand its behavior. The language most commonly (and conveniently) used to describe the natural world is mathematics. Therefore, to understand physics, we need to be fluent in the mathematics of the topics we'll study in this course… specifically basic algebra and trigonometry.
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;
