Методическое пособие по решению тригонометрических уравнений, Орлова Л.Г., Савельева А.Р., Кульжумиева А.А., 2017

Методическое пособие по решению тригонометрических уравнений, Орлова Л.Г., Савельева А.Р., Кульжумиева А.А., 2017.

   Методическое пособие предназначается для студентов педагогических специальностей, методистов и преподавателей университетов, учителей школ и учащихся при изучении данной темы и при подготовке к ЕНТ. Пособие особенно удобно для самостоятельной работы студентов и школьников. Приведены необходимые теоретические сведения и формулы. При составлении тестовых заданий использованы материалы, которые на протяжении ряда лет применялись на ЕНТ РК. Пособие может быть использовано в процессе обучения тригонометрии в вузе и школе.




Stages of trigonometry development as a science.
Trigonometry is one of the newest sections of elementary mathematics, received final clearance only in the XVIII century. Although some ideas it dates back to antiquity, to the ancient world and mathematical creativity Indians (K. Ptolemy II in., Al-Battani the IX. et al.). European mathematicians have reached a high degree of perfection in the calculation table of natural sciences and tangents (Regiomontanus XV century. Retikus and Pitiskus XVI c., Et al.).

The term "trigonometry" of Greek origin, signifying "measurement of triangles" (trigonon) - Triangle (metreyn) - measurement.

Scientific development of trigonometry performed by Euler in his work «Jntroductio in analysis infinitorum» (1748). He created as the science of trigonometry functions, gave it an analytical presentation, brought the entire set of formulas of the few basic formulas. Designation of parties and small letters opposing angles - corresponding capital letters allowed him to simplify all the formulas, clarify them and harmony. Euler thought belongs to consider the trigonometric functions as ratios of the corresponding lines to the radius of the circle, i.e. E. The numbers, with the radius of the circle as "full sine" he took the unit. Euler obtained a number of new relations established communication trigonometric functions with exponential, given the rule of signs functions for all quarters, was a generalized reduction formula trigonometry and freed from many mistakes made in almost all European textbooks of mathematics.

Contents.
PART ONE. Trigonometric equations in school mathematics.
1.1. Stages of trigonometry development as a science.
1.2. Solution of trigonometric equations.
1.2.1. Simple trigonometric equations and their solutions.
1.2.2. The question as sin2x=a; cos2x=a; tg2x=a; ctg2x=a.
1.2.3. Equations containing a trigonometric function of the same argument.
1.2.4. Equations containing various trigonometric functions of one and the same argument.
1.2.5. Equation, the left of which is decomposed into factors, and the right side is equal to zero.
1.2.5. Equation, the left of which is decomposed into factors, and the right side is equal to zero.
1.2.6. Homogeneous equation for the function sin x и cos x.
1.2.7. Equations of the form a sin x+b cos x = c.
1.2.8. Equations containing different function arguments.
PART TWO. Tasks for independent execution.
2.1. Exercises to consolidate the material.
2.1.1. Equations containing trigonometric functions of one and the same argument.
2.1.2. Equation including trigonometrical functions of different arguments.
2.2. Options control work.
2.2.1. First Embodiment.
2.2.2. Second Embodiment.
2.2.3. Third Embodiment.
2.3. The approximate test questions according to all sections of trigonometry which are found on UNT.
PART THIRD. REFERENCE MATERIAL.
3.1 Basic trigonometric formulas.
3.1.1. Main trigonometric identities.
3.1.2. Formulas of addition.
3.1.3. Formulas of double argument.
3.1.4. Formulas of the sum and difference
3.1.5. Formulas of a half comer (decrease of degree).
3.2. General formulas of the solution of the elementary trigonometric equations.
3.3. Inverse trigonometric functions.
3.4. The identities connecting the inverse trigonometric functions.



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Теги: учебник по математике :: математика :: Орлова :: Савельева :: Кульжумиева :: тригонометрия