1. Development of cognitive interest in learning.
2. The use of mathematical modeling as a way to activate analytical thinking.
3. Formation of practical skills in constructing graphs of functions based on the studied theoretical material.

1. Use the existing potential of knowledge about the properties of functions in specific situations.
2. Be able to defend your point of view.
3. Apply conscious connections between analytical and geometric models of trigonometric functions.

During the classes.

1. Organizational moment.

2. “Entering the lesson.”

There are 3 statements written on the board:

1) Trigonometric equations sin x = a, cos x = a, tan x = a, cot x = a always have solutions.

2) The graph of the trigonometric function y = f(-x) can be obtained from the graph of the function y = f(x) only using a symmetry transformation about the Oy axis.

3) A harmonic oscillation graph can be constructed using one main half-wave.

Students discuss in pairs: are the statements true? (1 minute). The results of the initial discussion (yes, no) are then entered into the table in the "Before" column.

The teacher sets the goals and objectives of the lesson.

3. Oral exercises (frontal ).

1) Check whether the points belong to the function graphs:

y = sin x point with coordinates

y = cos x point with coordinates .

2) Find the largest and smallest values ​​of the functions:

y = sin x on the segment

y = cos x on the half-interval

y = tan x on the half-interval

3) Solve the equations: cos x = 0, tan x = -1, sin x = 2.

4) Is the number 15? period of the functions: y = sin x, y = cos x, y = tan x?

Name the main period of these functions.

5) Using Figures 14-17 on page 38 of the problem book, create analytical models of functions using graphs.

4. Warm-up (independently, with checking at the board).

No. 216(b). Solve graphically the equation sin x + cos x = 0.

5. Practical work No. 1(work on prepared models in 4 groups, groups are composed according to the level of preparedness of students).

1 group. No. 210 (g). How many solutions does the system of equations have?

2nd group. No. 183 (b). Solve graphically the equation sin x = x 2 + 1.

3rd group. No. 209 (c). Solve the equation graphically

4 group. How many solutions does the equation sin 2x = tan x have on the segment

(Check and discussion on layouts).

Practical work No. 2 (independent work on pieces of paper, 4 options, assignments are compiled according to the level of preparedness of students).

Graph the function:

7. Generalization and summing up.

No. 194 (b,c). Build and read the graph of the function y = f(x), where

8. Lesson summary. We return to the statements (beginning of the lesson), discuss using the properties of trigonometric functions, and fill in the “After” column in the table.

State autonomous professional

educational institution

"Orsk Medical College"

Methodological development in the discipline

ODB.06 Mathematics

Subject:

COMPILATED REVIEWED

at a meeting of the Central Committee

Mathematics teacher: general humanities,

I.V. Abroskina mathematical and

natural sciences

Protocol No.____

from___________2016

Chairman of the Central Committee:

T.V. Gubskaya

Orsk, 2016

EXPLANATORY NOTE

The Federal State Educational Standard is based on a system-activity approach. The Federal State Educational Standard sets new challenges for teachers.

development and education of the individual in accordance with the requirements of the modern information society;

developing students’ ability to independently receive and process information on educational issues;

individual approach to students;

development of communication skills among students;

orientation towards the use of a creative approach in the implementation of teaching activities.

The system-activity approach as the basis of the Federal State Educational Standard helps to effectively implement these tasks. The main condition for implementing the standard is the inclusion of students in such activities, when they will independently carry out an algorithm of actions aimed at obtaining knowledge and solving the educational tasks assigned to them. The system-activity approach as the basis of the Federal State Educational Standard helps develop children's abilities for self-education.

Within the framework of this approach, the theme "Trigonometric functions, their properties and graphs."

The methodological development is based on the Work Program (Federal State Educational Standard, specialty 02/34/01 Nursing, 02/31/03 Laboratory Diagnostics), according to which 2 hours of practical training are allocated to study the topic “Trigonometric functions, their properties and graphs”. The topic examines the basic properties of trigonometric functions and their graphs, the connection of these functions with medicine and other areas of knowledge, and emphasizes the importance of this topic.

While mastering the topic “Trigonometric functions, their properties and graphs,” students become aware of the role of mathematics and trigonometry in medicine, namely by deciphering the cardiogram of the heart, learn to calculate heart rate (heart rate), and recognize sinus rhythm (normal, tachycardia, bradycardia).

When studying this topic, there is a connection with medicine, biology, anatomy, which certainly motivates students to study this topic, and allows them to further deepen their knowledge of the subject.

In the process of studying the topic “Trigonometric functions, their properties and graphs,” students will be able in real life and in their professional activities to determine the heart rate from the cardiogram of the heart and make a conclusion about the nature of sinus rhythm.

Topic: Trigonometric functions, their properties and graphs

Know all the properties of trigonometric functions, be able to build graphs of trigonometric functions. Be able to draw a conclusion from a cardiac cardiogram about sinusoidal rhythm and heart rate.

Educational:

yfromx

Educational:

Cultivate accuracy, dedication, discipline.

continue to foster activity, mutual assistance, and a creative attitude to business.

Training aids, equipment

Outline, computer, projector, presentation.

Type of training session

Theoretical and practical

Technologies used

System-activity approach, information technology, problem-based learning technology.

Lesson structure

Stage 1.

Organizing time / 1-2 minutes

Student activities

Preparation for class

Teacher's activities

Checking those present, getting ready for the lesson

Stage 2.

Motivational moment / 2 minutes

Student activities

Formulating the purpose of the lesson

Teacher's activities

1. Formulates the topic of the lesson

2. Leads students to formulate the purpose of the lesson

3. Arouses interest in the material being studied using various methods 4. Creates motivation

Stage 3.

Frontal survey / up to 8 minutes

Student activities

Answer questions

Teacher's activities

Stage 4.

Learning new material /50 minutes

Student activities

1. Work with notes, write down the main points indicated by the teacher in a notebook

2. Independent description of the properties of trigonometric functions using a graph

3. Trigonometry in human life; Relationship between trigonometry and medicine, research work (presentations) - 2 groups of students

Teacher's activities

Explanation of new material:

1. Statement of the problematic question:

What is the importance of trigonometry for medicine?

2. Function type (definition, graph)

3. Function of the form (definition, graph

4. Showing the video “Everyone can do an ECG”

Stage 5.

Stage of consolidation and generalization of knowledge / 20 minutes

Student activities

1. Work in groups. Creation of a “consilium” of doctors and drawing up a conclusion on a cardiac cardiogram about sinusoidal rhythm and heart rate (HR)

2. summing up, recording conclusions in a notebook

Teacher's activities

1.Help in formulating conclusions

2. Monitoring and correction of knowledge, providing the opportunity to identify the causes of errors and correct them.

Stage 6.

Reflection /6 minutes

Student activities

.

2.Work with notes

Notes in the margins:

“+” - knew

"!" - new material (learned)

"?" - I want to find out

Teacher's activities

Monitoring the results of educational activities, assessing knowledge.

Stage 7.

Homework / 2 minutes

Contents of homework

Without knowledge of mathematics you cannot understand the basics

modern technology, not how scientists study

natural and social phenomena.

A.N. Kolmagorov

Lesson on the topic : Trigonometric functions, their properties and graphs.

Organizational information

Lesson topic: Trigonometric functions, their properties and graphs

Item: Mathematics

Teacher: Abroskina Irina Vladimirovna

Educational institution: GAPOU "Orsk Medical College"

Methodological base:

1. Lukankin A.G. - Mathematics: textbook. for middle school students prof. education / A.G. Lukankin. - M.: GEOTAR - Media, 2012. - 320 p.

2. Mordkovich A.G. - Algebra and beginnings of analysis. 10-11 grades: Textbook. for general education institutions. - M.: Mnemosyne, 2012. - 336 p.

3. Studies.ru

4. Math. ru"library"

5. History of mathematics from ancient times to the beginning of the 19th century in 3 volumes // ed. A. P. Yushkevich. Moscow, 1970 – volume 1-3 E. T. Bell Creators of mathematics.

6. Predecessors of modern mathematics // ed. S. N. Niro. Moscow, 1983 A. N. Tikhonov, D. P. Kostomarov.

7. Stories about applied mathematics // Moscow, 1979. A.V. Voloshinov. Mathematics and art // Moscow, 1992. Newspaper Mathematics. Supplement to the newspaper dated September 1, 1998.

Lesson type: combined

Duration: 2 class hours

The purpose of the lesson: Study of trigonometric functions, their properties and graphs.

Determining the role of trigonometry for medicine.

Lesson objectives:

Educational : Know all the properties of trigonometric functions, be able to build graphs of trigonometric functions. Be able to draw a conclusion from a cardiac cardiogram about sinusoidal rhythm and heart rate.

Educational: Continue developing skills in plotting graphs using dependenciesyfromx. Show the importance of trigonometry for medicine.

Educational: Cultivate accuracy, dedication, discipline. Pcontinue to give birthfostering activity, mutual assistance, and a creative attitude to business.

Technologies used: system-activity approach, developmental training, group technology, elements of research activities, ICT.

Equipment and materials for the lesson: computer, projector, student presentations, video “An ECG can be done by everyone”

Lesson plan:

1. Organizational moment - 1-2 minutes.

2. Motivational moment - 2 min.

3. Frontal survey - 8 min.

4. Studying new material - 50 min.

5. Consolidation and generalization of knowledge - 20 min

6. Reflection - 6 min.

7. Homework - 2 min.

During the classes

1. Organizational moment

Checking those present, getting ready for the lesson.

2. Motivational moment

Lesson topic message

Leading students to independently formulate the purpose of the lesson

Emphasizing the importance of this topic for medicine and the world around us.

3. Frontal survey

Answers to questions on homework (analysis of unsolved problems)

Students' answers to teacher's questions ( At this stage, students’ knowledge necessary for further work in the lesson is updated):

1. What are trigonometric functions of a numeric argument?

2. What is the value of trigonometric functions in the first quarter (table of values)?

3. Which functions are even and which are odd?

4. What is the symmetry of the graphs of even and odd functions?

5. Which of the trigonometric functions are even (odd)?

4. Learning new material

1) I would like to start studying the topic with the words of the great mathematician Nikolai Ivanovich Lobachevsky: "There is not a single branch of mathematics that will someday not be applicable to the phenomena of the real world."

2) Let’s pose the question: What is the significance of trigonometry for medicine?

I hope that after studying our topic, each of you will be able to answer the question posed.

3) So, let's start studying trigonometric functions, consider their basic properties and build their graphs.

Trigonometric functions

The main trigonometric functions are the functions y=sin(x), y=cos(x), y=tg(x), y=ctg(x). Let's consider each of them separately.

Y = sin(x)

Graph of the function y=sin(x).

Basic properties:

3. The function is odd.

Y = cos(x)

Graph of the function y=cos(x).

Basic properties:

1. The domain of definition is the entire numerical axis.

2. Function limited. The set of values ​​is the segment [-1;1].

3. The function is even.

4. The function is periodic with the smallest positive period equal to 2*π.

Y = tan(x)

Graph of the function y=tg(x).

Basic properties:

1. The domain of definition is the entire numerical axis, with the exception of points of the form x=π/2 +π*k, where k is an integer.

3. The function is odd.

Y = ctg(x)

Graph of the function y=ctg(x).

Basic properties:

1. The domain of definition is the entire numerical axis, with the exception of points of the form x=π*k, where k is an integer.

2. Unlimited function. The set of values ​​is the entire number line.

3. The function is odd.

4. The function is periodic with the smallest positive period equal to π.

4) Why does a person need knowledge of the properties of functions and the ability to read graphs in life?Any periodically repeated movement is calledOSCILLATIONS

The practice of studying oscillations has shown both a beneficial and harmful role.

Every specialist needs to master the theory of oscillatory processes.

Oscillation theory is a field of science related to mathematics, physics and medicine.Harmonic vibrations

Mechanical vibrations

Vibration. Harmful effects of vibration

Ultrasound

Infrasound sound

Electromagnetic vibrations (used for radio, television,

communications with space objects)

Conclusion :

Oscillations occur according to the laws of sines and cosines

Properties of trigonometric functions show which parameters can change

Measurement results and calculations show how to avoid the harmful effects of vibrations and how to apply them

5) Let us dwell in more detail on the theory of oscillations in medicine. Where do you encounter fluctuations in your body -HEART. What is a heart cardiogram called?SINE SOIDE. Consequently, the heart works according to trigonometric laws, and we simply need to know and understand them.

Trigonometric laws are also found in the world around us:

In nature (biology)

In architecture (buildings, structures)

In music (harmonious melodies)

and in other areas.

Now, a group of students will present to you their research works on this topic. Presentation of presentations by students on the topics:

- "Relationship of trigonometric function and medicine"

- "Trigonometry in medicine"

- "Trigonometry in the world around us and human life"

6) Watching the educational video “Everyone can do an ECG”

7) Introducing students to the ECG of a healthy person and rhythm disturbances.

8) Formula for calculating heart rate (heart rate)

5. Consolidation and generalization of knowledge

1. Divide students into 2 groups.

2. Work in groups. Creation of a “consilium” of doctors and drawing up a conclusion on a cardiac cardiogram about sinus rhythm and heart rate (HR)

3. Voice your conclusions (one representative from the group)

4. Main conclusions, correction by the teacher of the main conclusions.

6. Reflection

1. Independent summing up of the lesson, self-analysis and self-assessment.

2. Working with notes

Notes in the margins:

“+” - knew

"!" - new material (learned)

"?" - I want to know

3. Knowledge assessment.

7. Homework

1. Mathematics, Bashmakov M.I., 2012 - Page 107/Page 165

2. Prepare (optional) a message: “Trigonometry in medicine and biology”

Lesson appendix

Student presentations

(research groups)

Class: 10

The purpose of the lesson:

• Educational:
  • practice skills in constructing graphs of functions using the periodicity of trigonometric functions;
  • consolidate the material learned about even and odd functions
• Educational:
  • develop skills, analyze, and apply existing knowledge of students in a changed situation.
• Educational:
  • to cultivate in students accuracy, curiosity, respect for the world around them, and moral qualities;
  • create conditions for the development of cognitive activity of students, the implementation of the personal functions of each student, his free development, taking into account individual characteristics and potential capabilities.

Equipment:

• multimedia projector;
• student assignment sheets;
• score sheets;
• board;
• chalk, drawing tools;
• notebooks;
• coordinate system blanks

DURING THE CLASSES

I. Organizational moment

Students, when entering the classroom for a lesson, choose tokens in which the trigonometric functions sine, cosine, tangent are written. Then they are seated at round tables in groups with tokens of the same function.

The objectives of the lesson are announced. Throughout the lesson, students independently evaluate their preparation for the lesson. To do this, each group is given assessment sheets; the criteria for assessing their activities at each stage of the lesson are reflected on the slides ( Annex 1 ).
Evaluation sheets are filled out by students and submitted at the end of the lesson along with their written work for checking.

Evaluation paper

II. Frontal survey “Theoretical warm-up”

In order to complete the practical tasks of the lesson, you need to remember the theoretical material. To do this, we will carry out "Theoretical warm-up" on the slide ( Annex 1 ) a table with question numbers is given, in turn each group selects a question number, reads out the question and immediately gives an answer to it.

At this stage, students’ knowledge necessary for further work in the lesson is updated.

1. What is a function called?
2. What is the domain of a function called?
3. What is the range of a function called?
4. Which function is called even?
5. Which function is called odd?
6. What properties does the graph of an even function have?
7. What properties does the graph of an odd function have?
8. Define basic trigonometric functions.
9. What can you say about the parity of trigonometric functions?
10. Which function is called periodic?
11. Which number is the smallest positive period for the sine and cosine function?
12. What number is the smallest positive period for the tangent (cotangent) function?
13. What is the domain of definition of the sine function?
14. What is the domain of the cosine function?
15. What is the domain of the tangent function?
16. What is the domain of the cotangent function?
17. What is the range of the sine function?
18. What is the range of the cone function?
19. What is the range of the tangent function?
20. What is the range of the cotangent function?
21. Which of the functions takes the greatest value y = sin 2x or y = 2 sin x&

– We repeated the theoretical material with you. And now I suggest you show your knowledge in determining an even or odd function by performing the “mathematical lotto”. Each group receives a sheet - a task with a “mathematical lotto”. ( Appendix 2 ).

Exercise: in the resulting table, shade those cells in which the even (odd) function is located.

"Mathematical Lotto"

Option 1.

Exercise: Shade in the table those cells in which the even function is located

Option 2.

Exercise: Shade in the table those cells in which the odd function is located

Evaluation criteria for frontal survey, participation in class collaboration:

• 2 points, did not actively participate;
• 3 points, answered questions, made suggestions when completing the “mathematical lotto” task
• 4 points, actively answered questions, offered correct answers when solving the “mathematical lotto”

III. Work in groups on plotting trigonometric functions

Working together in a group on a task, the student correlates his “I” with himself and those around him, comparing different or identical visions of the task and the process of solving it, assessing his capabilities and aspirations. Students have to act in different roles both in the role of “student” and in the role of “teacher”. Here the ability to work in a group, the ability to defend one’s point of view and accept the point of view of comrades is formed.

Each group is asked to independently construct graphs of trigonometric functions in their notebooks, having previously determined its domain of definition, domain of value, and period. Each group also receives coordinate system blanks on an A4 or A3 sheet of paper on which they need to depict the completed task (you can use felt-tip pens of different colors when constructing graphs)

After completing their assignment, each group defends their work in front of the class. The work of everyone in the group is assessed by the whole group, and the assessment is recorded on the score sheet.
Criteria for assessing group work:

• 3 points, did not actively participate in the work;
• 4 points, made suggestions to solve the problem;
• 5 points, actively participated in the work of the group, suggested the right ways to solve the problem.

IV. Test work

Before students begin taking the test, they must select a difficulty level that matches their abilities.
At this stage of work, a situation is created for students in which they need to evaluate their real knowledge and capabilities.

1) If a student believes that he has mastered the material to a “3” level, then he only needs to complete 1–5 tasks of the test.
2) If you have mastered the material with a “4”, then you need to complete 6–7 tasks of the test.
3) If the material has been mastered at “5”, then you must complete all test tasks.

Key to the test:

Notebooks and assessment sheets are handed over to the teacher.

V. Lesson summary

Grades are given in the journal after the teacher checks the work, comparing it with the results of the knowledge assessment sheets.

VI. Homework

Group I: page 93 No. 18
Group II: page 93 No. 19
III group: page 93 No. 20

Algebra and beginnings of analysis grade 10 UMK: A.G. Mordkovich Algebra and beginnings of mathematical analysis grades 10-11 in 2 hours. Part 1. Textbook; A.G. Mordkovich Algebra and beginnings of mathematical analysis grades 10-11 in 2 hours. Part 2. problem book; A.G. Mordkovich, P.V. Semenov Algebra and beginnings of mathematical analysis grades 10-11. Methodological manual for teachers. Level of learning: basic Lesson topic: Repetition. Trigonometric functions and their properties The total number of hours allocated for the final generalization repetition is 12 hours. 3 hours are allotted for generalization and repetition of this topic “Trigonometric functions and their properties”. Lesson No. 1 Objectives: Educational: summarize and systematize students’ knowledge on the topic studied, monitor the level of mastery of the material; Developmental: development of mathematical thinking, intellectual and cognitive abilities, development of the ability to justify one’s decision, control and evaluate the results of one’s actions; Educational: nurturing a culture of communication, cognitive activity, a sense of responsibility for the work performed, discipline, accuracy, and independence. Objectives: Generalize the idea of ​​the number circle, the number circle on the coordinate plane. Practice the ability to find the value of sine and cosine on the number circle. Practice the skills and abilities of constructing graphs of functions. Develop creativity in graphing functions and knowing. As a result of studying this topic: Students develop key competencies - the ability to act independently in situations of uncertainty when solving problems that are relevant to them - the ability to be motivated to refuse a sample, to look for original solutions Students demonstrate theoretical and practical knowledge on the topic: the ability to plot trigonometric functions graphs and descriptions their properties. They are able to substantiate judgments in detail. Can critically evaluate information adequately for the purpose set. Students can freely use the properties of functions and graph complex functions. They are able to convey information concisely, completely, selectively. They are able to self-assess their own actions. They are able to independently select criteria for comparison, comparison, evaluation and classification of objects. Equipment and materials for the lesson: multi-projector, presentation to accompany the lesson, self-control sheets, cards with the text of independent work. Lesson type: training lesson Lesson progress. I. Organizational moment. II. Reporting the topic and goals of the lesson Today in the lesson we will summarize and systematize existing knowledge on the topic “Trigonometric functions and their properties.” And all knowledge must turn into skill and skill. We will test our knowledge, skills and abilities, find out the gaps and try to eliminate them. Today we will remember how to determine the value of a function by the value of the argument using different ways of specifying the function; build graphs of the studied functions; describe the behavior and properties of functions using a graph and, in the simplest cases, using a formula; find the largest and smallest values ​​from a graph of a function. III. Updating basic knowledge. Work with cards Option No. 1 Option No. 2 1. Construct a graph of the function; 2. Specify the range of values ​​of this function; 3. Find the largest and smallest values ​​of the function on interval 1. Plot a graph of the function; 2. Indicate the intervals of increase and decrease of the function; 3. Determine the zeros of the function. We check and compare functions. What properties of trigonometric functions did you use when solving problems? Option 1: y=sinx, pay attention to the slide. Domain of definition Points of intersection with coordinate axes Even and odd Intervals of monotonicity Extrema Periodicity Intervals of constancy of sign Set of values ​​Option 2: y=cos x, attention to the slide. Domain of definition Points of intersection with coordinate axes Even and odd Intervals of monotonicity Extrema Periodicity Intervals of constant sign Set of values ​​IV. Workshop on solving problems 1. In one coordinate system, construct graphs of functions of one group and describe their properties: 1) , . 2) , . Generalize transformations of function graphs by shifting along the axis. In one coordinate system, construct graphs of functions of one group and describe their properties: 1) , . 2) , . 2. Prove that the number is the period of the function. 3. Prove that the number is the period of the function. 4. Find the smallest positive period of the function 5. Find the smallest positive period of the function 6. Convert from degrees to radians and arrange in ascending order: , . 7. Convert from radian measure to degree measure and arrange in descending order: , . V. Lesson summary VI. Review the properties of tangent and cotangent.

Download:

Preview:

Algebra and the beginnings of analysis

Grade 10

UMK: A.G. Mordkovich Algebra and beginnings of mathematical analysis grades 10-11 in 2 hours. Part 1. Textbook;

A.G. Mordkovich Algebra and beginnings of mathematical analysis grades 10-11 in 2 hours. Part 2. problem book;

A.G. Mordkovich, P.V. Semenov Algebra and beginnings of mathematical analysis grades 10-11. Methodological manual for teachers.

Level of training: basic

Lesson topic: Repetition. Trigonometric functions and their properties

The total number of hours allocated for the final generalization repetition is 12 hours. 3 hours are allotted for generalization and repetition of this topic “Trigonometric functions and their properties”.

Lesson #3

Goals:

Educational: summarize and systematize students’ knowledge on the topic studied, monitor the level of mastery of the material;

Developmental: development of mathematical thinking, intellectual and cognitive abilities, development of the ability to justify one’s decision, control and evaluate the results of one’s actions;

Educational: nurturing a culture of communication, cognitive activity, a sense of responsibility for the work performed, discipline, accuracy, and independence.

As a result of studying this topic:

Students develop key competencies - the ability to act independently in situations of uncertainty when solving problems that are relevant to them - the ability to be motivated to refuse a model, to look for original solutions

Students are demonstrated theoretical and practical knowledge on the topic: the ability to construct graphs of trigonometric functions and describe their properties. They are able to substantiate judgments in detail. Can critically evaluate information adequately for the purpose set.

Students can freely use the properties of functions and graph complex functions. They are able to convey information concisely, completely, selectively. They are able to self-assess their own actions. They are able to independently select criteria for comparison, comparison, evaluation and classification of objects.

Equipment and materials for the lesson: multi-projector, presentation to accompany the lesson, self-control sheets, cards with the text of independent work.

Lesson type: knowledge review lesson

During the classes.

I. Organizational moment.

II. Communicating the topic and objectives of the lesson.

The strongest is the one who controls himself.
Seneca

We live in the real world and to understand it we need knowledge. But before we rise to the next step, we need to make sure that we stand firmly on our feet and have good, solid knowledge on the topic being studied.

Today in the lesson we will summarize and systematize existing knowledge on the topic “Trigonometric functions and their properties.”

And all knowledge must turn into skill and skill. We will test our knowledge, skills and abilities, find out the gaps and try to eliminate them.

1. Updating basic knowledge.

1. Frontal survey.

What are the trigonometric functions you know?

Now let's repeat the properties of the trigonometric functions known to us.

(Teachers name the properties of trigonometric functions, each correct answer is displayed on the slide. As a result of the discussion, a table appears.) (Slide 4-7)

2. Oral work on solving simple problems on transforming graphs of trigonometric functions. (Slide 8-10)

1. Working with self-control sheets. (Appendix 1, slide 11)

During the lesson you will perform various tasks, and gradually fill out the student’s self-control sheet. Sign the self-control sheet and become familiar with its contents. Assess how ready you are to complete tasks and give a predictive rating. And set the sheet aside for now.

1. Graphic dictation.

The result of completing the dictation on students’ self-control sheets will be the following entry.

where the signs indicate: + yes,No. After finishing the dictation, the teachers exchange the dictation with their neighbor at the desk for checking. Each correct answer is scored 1 point; incorrect answers and no answers are scored 0 points. Slide 12

1. Independent work on options. (Appendix 2)

I option.

y = 4 x.

1. Determine the sign of the number sin1 cos9 tan(-2)

1. no intersection points

1. Find the smallest positive period of the function

y=2+

Option II.

1. Specify multiple function values: