- •Часть II
- •050100.62 «Педагогическое образование»,
- •Рецензенты: Лихачева о. Е.,
- •Юдина н. В.,
- •Введение
- •Рекомендации студентам по работе с учебными текстами по специальности
- •1. Произношение и чтение
- •2. Работа с лексикой
- •3. Работа над упражнениями
- •Algebra. Geometry text 1
- •The nature of algebra
- •Exercises:
- •1. Read the following words paying attention to the pronunciation:
- •2. Form nouns and translate them into Russian:
- •4. Express agreement or disagreement with the following:
- •5. Insert the missing words.
- •6. Translate into Russian.
- •7. Answer the following questions:
- •Definitions and notations
- •Exercises:
- •6. Translate into English:
- •Algebraic signs
- •Exercises:
- •6. Translate into English:
- •Squares and square roots
- •Exercises:
- •Involution
- •8. Translate into English:
- •Monomial and polynomial
- •Exercises:
- •2. Point out the nouns, adjectives and adverbs and write them down in three columns:
- •3. Give Russian equivalents to:
- •4. Choose the right word:
- •5. Answer the following questions:
- •6. Translate into English.
- •7. Make up 10 questions of all five types to the text. Ask your fellow-student to answer them. Text 6
- •Points and lines
- •Exercises:
- •Solid geometry
- •6. Translate into English:
- •7. Insert the missing words.
- •Kinds of angles
- •Exercises:
- •1. Read the following words paying attention to pronunciation:
- •3. Answer the following questions:
- •4. Express agreement or disagreement with the following:
- •6. Make up sentences of your own using words and expressions given below:
- •7. Translate into Russian.
- •8. Translate into English:
- •Measurement of angles
- •Exercises:
- •1. Make up sentences of your own using the words and expressions given below:
- •2. Answer the following questions:
- •4. Read the text. Ask 5 questions to it:
- •5. Translate into Russian:
- •6. Translate into English:
- •Exercises
- •Geometric solids
- •7. Answer the following questions:
- •8. Translate into Russian:
- •9. Choose the right word:
- •10. Read and translate. Theorems of Solid Geometry
- •Text 10
- •Kinds of polygons
- •Exercises:
- •Text 11
- •Trigonometry
- •Exercises:
- •Text 12
- •Trigonometric functions
- •Exercises:
- •7. Translate into English:
- •Text 13
- •Tables of values of trigonometric functions
- •Exercises:
- •6. Translate into English:
- •Основная литература
- •Периодические издания
- •Интернет-ресурсы
- •Рейтинговая система оценки успеваемости студентов 1 курса 2 семестр
Text 12
При работе над текстом “Trigonometric functions” формируется компетенция ОК-10: владеет одним из иностранных языков на уровне, позволяющем получать и оценивать информацию в области профессиональной деятельности из зарубежных источников.
В рамках формирования компетенции у студентов вырабатываются следующие умения, навыки:
Уметь
понимать информацию текстов из учебной литературы в соответствии с конкретной целью;
выступать с подготовленным сообщением.
Владеть
навыками оформления речевых высказываний в соответствии с грамматическими и лексическими нормами устной и письменной речи, фонетическими нормами (устная речь) и основными правилами орфографии и пунктуации (письменная речь) иностранного языка, не допуская ошибок, препятствующих речевому общению;
навыком использования двуязычных словарей при чтении различного типа текстов;
профессиональными основами речевой коммуникации с использованием терминологии данной дисциплины.
Применяются интерактивные технологии: работа малыми группами, решение ситуационных задач.
Trigonometric functions
Trigonometry is based on certain "functions" of angles. A function is a quantity that depends on another quantity for its value. Any quantity that depends upon an angle for its value is the function of that angle. If a right triangle is constructed, having a certain angle at one corner, there will be certain definite relations between the sides of this triangle.
These ratios are six in number and are called the trigonometric functions.
In any right triangle, we call the two lines that form the right angle the sides, while the line opposite the right angle is called the hypotenuse. One of two other sides is called opposite side, while the other is called the adjacent side. The ratio of the opposite side to the adjacent side is called the tangent of the angle. The ratio of the adjacent side to the opposite side is called the cotangent.
In any right triangle, the sine of either acute angle is the ratio of the side opposite the angle to the hypotenuse.
In any right triangle, the cosine of either acute angle is the ratio of the adjacent side to the hypotenuse.
The secant of the angle is the reciprocal of the cosine, that is, it is reverse ratio of the cosine. In a right triangle, the secant of an angle is the ratio of the hypotenuse to the side adjacent to the angle.
The cosecant is the reciprocal of the sine; that is there verse ratio, being the ratio of the hypotenuse to the side opposite the angle.
Exercises:
1. Read the following words paying attention to the pronunciation: height, identify, satisfy, sine, cosine, combine, secant, cosecant, tangent, cotangent.
2. Add suffixes to the words given below and translate them into Russian:
- wise: clock, counterclock, other;
- tion: relate, opposite, abbreviate, definite;
- ing: write, call, construct, shorten.
3. Make up sentences of your own using the words and expressions given below:
to be based on, to depend on, for its value, is constructed, five in number, hypotenuse, opposite side, adjacent side.
4. Answer the following questions:
1. What is a trigonometric function?
2. What lines in any right triangle are called sides?
3. What is called the tangent of the angle?
4. What is called the cotangent?
5. What is the sine of an angle?
6. What is the cosine of an angle?
7. What is the secant of an angle?
8. What is the cosecant of an angle?
5. Translate into Russian:
We find that the values of the right triangle ratios depend only on angles and that to each different angle there corresponds a different set of those values. Any number or quantity is called a function of that second number or quantity. Therefore, the right triangle ratios are functions of the acute angles of the triangle.
6. Read and translate the Laws of Sines and Cosines. Learn them by heart:
The Law of Sines. In a triangle any side is to any other side as the sine of the angle opposite the first side is to the sine of the angle opposite the other side; or, if a and b be the sides, and A and B the angles opposite them:
a/b = sin A/ sin B
The Law of Cosines. In a triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle; or if a, b and c be the sides and the angle opposite side a be denoted A, then: a2 = b2+ c2 - 2bc cos A.