The relationship between the sine, cosine and tangent of the same angle. Lesson 4 - презентация, доклад, проект скачать

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The relationship between the sine, cosine and tangent of the same angle. Lesson 4, слайд №1

The relationship between the sine, cosine and tangent of the same angle. Lesson 4, слайд №2

The relationship between the sine, cosine and tangent of the same angle. Lesson 4, слайд №3

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The relationship between the sine, cosine and tangent of the same angle. Lesson 4, слайд №7

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Слайды и текст этой презентации

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The relationship between the sine, cosine and tangent of the same angle. Topic of lesson:

Слайд 2

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The goal of lessons: Education: concluded basic trigonometric identities; training in the use of these formulas to calculate the values of the sine, cosine of the number specified by the value of one of them. Developing: learn to analyze, compare, build analogy, summarize and organize, define and explain the concepts. Educational: education conscientious attitude to work and a positive attitude towards learning.

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Material needed: textbooks, notebooks, table, computer, screen, projector.

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Type of lesson: Combined

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Lesson Plan: 1. Organization of the beginning of the lesson (2-3 min.). 2. Survey and repetition ( Definition of sine, cosine and tangent and their signs) (10 min.). 3. Explanation of the new material (10 min.). 4. Attaching a new material (15 min.). 5. Setting the home (3-4 min.).

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Proceduses (Ход урока)

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1. Organization of the beginning of the lesson (2-3 min.). Good afternoon, boys and girls! Sit down, please. Who is absent today?

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2. Survey and repetition ( Definition of sine, cosine and tangent and their signs) (10 min.). Specify signs of trigonometric functions of these angles: 2. Find the value of the expression

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Answers 1. 2.

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3. Explanation of the new material (10 min.). As already known in the ordinate and abscissa x can be represented in the form of sine and cosine of the angle by the following formulas: sin(a) = у, cos(a) = х. Substituting these values into the equation of the unit circle we have the following equality: (sin(a))2 + (cos(a))2 =1 This equality holds for all values of the angle a. It is called the Pythagorean trigonometric identity. From the basic trigonometric identities can be expressed by one function over another. sin(a) = ±√(1-(cos(a))2), cos(a) = ±√(1-(sin(a))2).

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For example. Calculate sin (a), if the cos (a) = - 3/5 and <a <3 * / 2. We use the above formula: sin (a) = ± √ (1- (cos (a)) 2). Since <a <3 * / 2, a 3 quarter, the sign in front of the root will be "minus". Sin is negative in the third quarter. sin (a) = ± √ (1- (cos (a)) 2) = - √ (1 - 9/25) = - 4/5.