Plotting the cosine presentation function. Graphs and properties of trigonometric sine and cosine functions. III. Verification work

"Function y = cos x" - Zeros of the function, positive and negative values. Let's find some points for plotting. Y = cos (x - a). Transformation of the graph of the function y = cos x. Function y = cos x. Y = cos x + A (properties). Properties. Symmetrical reflection about the abscissa axis. Function graph. Even, odd.

"Properties of inverse trigonometric functions" - Specify the range of values ​​of the function. Solve equations. Find the meaning of the expression. Solving equations. Group work. Elective course in mathematics. Arc functions. Let's solve the system of equations. Research... Specify the scope of the function. Repetition. The triple satisfies the original equation.

"Functions of tangent and cotangent" - Properties of the function y = tgx. Solutions. Equation roots. Schedule. Building a graph. Function properties. Meaning. Fraction. The main properties of the function. Function y = tgx. Basic properties. y = ctgx. Function graph y = ctgx. Numbers.

"Convert trigonometric graphs" - Sine function. Converting charts trigonometric functions... The characteristic of the graph of the harmonic oscillation. Graph of the function y = f (x) + m. Cosine function. Graph of the function y = f (| x |). Graph of the function y = | f (x) |. Characteristic of transformations of graphs of functions. Y = f (x). Tangent function. Plots of the resulting schedule.

"Arcfunctions" - Functional-graphic method for solving equations. Arctgx. Function. Trigonometric functions. Properties of arc functions. Y = arcctgx. Arcctg t = a. Arccosx. Graphical method for solving equations. Range of values. Equality. Definitions. Expression. Definition. Arctg t. Arccos t. Lots of real numbers.

"Algebra" Trigonometric functions "" - Trigonometric functions of an angular argument. Table of values ​​of trigonometric functions of some angles. A guide to algebra and the beginnings of analysis. Solution of trigonometric inequalities. Solving trigonometric equations. Converting sums of trigonometric functions into products. Trigonometry.


Graphs and properties of trigonometric functions of sine and cosine Graph of the function y = sinx Graph function y = sinx Properties of function y = sinx Properties of function y = sinx Graph of function y = cosx Graph of function y = cosx Properties of function y = cosx Properties of function y = cosx Comparison of properties of functions y = sinx and y = cosx Comparison of properties of functions y = sinx and y = cosx















Properties of the function y = sinx 6. Intervals of constant sign of the function y = sinx: sinx> 0 for x (2k; + 2k), sinx 0 for x (2k; + 2k), sinx 0 for x (2k; + 2k), sinx 0 for x (2k; + 2k), sinx 0 for x (2k; + 2k), sinx title = "(! LANG: Properties of the function y = sinx 6. Sign intervals of the function y = sinx: sinx> 0 for x (2k; + 2k), sinx














Properties of the function y = cosx 6. Intervals of constant sign of the function y = cosx: cosx> 0 for x (- / 2 + k; / 2 + k), k cosx 0 for x (- / 2 + k; / 2 + k), k cosx 0 for x (- / 2 + k; / 2 + k), k cosx 0 for x (- / 2 + k; / 2 + k), k cosx 0 for x (- / 2 + k; / 2 + k), k cosx title = "(! LANG: Properties of the function y = cosx 6. Intervals of constant sign of the function y = cosx: cosx> 0 for x (- / 2 + k; / 2 + k), k cosx




Comparison of the properties of the functions y = sinx and y = cosx Function y = sinxy = cosx Domain D (sinx) = D (cosx) = Set of values ​​E (sinx) = [-1,1] E (cosx) = [-1,1] Even and odd odd odd even Zeros of the function x = k, kx = / 2 + k, k Intervals of constant sign y (x)> 0 x (2k; + 2k) x (- / 2 + k; / 2 + k) ky (x ) 0 x (2k; + 2k) x (- / 2 + k; / 2 + k) ky (x)

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Slide captions:

Function y = sin x, its properties and graph. Lesson objectives: To review and systematize the properties of the function y = sin x. Learn to plot the function y = sin x.

y = sin x Domain of definition - the set R of all real numbers: D (f) = (- ∞; + ∞) Property 1.

y = sin x Since sin (-x) = - sin x, then y = sin x is an odd function, which means its graph is symmetric about the origin. Property 2.

y = sin x The function y = increases on the segment and decreases on the segment [π / 2; π]. Property 3.0 π / 2 π

y = sin x The function y = sin x is bounded both from below and from above: - 1 ≤ sin x ≤ 1 Property 4.

y = sin x y naim = -1 y naib = 1 Property 5. 0 π / 2 π

Let us construct a graph of the function y = sin x in the rectangular coordinate system Oxy.

y 0 π / 2 π x

First, let's build a part of the graph on a segment. -2 π -3 π / 2 - π - π / 2 0 π / 2 π 3 π / 2 2 π X 1 -1 Y x 0 π / 6 π / 3 π / 2 2 π / 3 5 π / 6 π y 0 1/2 √ 3/2 1 √ 3/2 1/2 0 Now draw a part of the graph on the segment [- π; 0], taking into account the oddness of the function y = sin x. On the segment [π; 2 π] the graph of the function looks like this again: And on the interval [-2 π; - π] the graph of the function looks like this: Thus, the whole graph is a continuous line, which is called a sinusoid. Sine arc Half sine wave

No. 168 - orally. -3 π -5 π / 2 -2 π -3 π / 2 - π - π / 2 0 π / 2 π 3 π / 2 2 π 5 π / 2 3 π Х У 1 -1

Solve exercises 170, 172, 173 (a, b). Homework: No. 171, 173 (c, d)


On the subject: methodological developments, presentations and notes

Interactive test, which contains 5 tasks with the choice of one correct answer out of four proposed, taking into account the time spent on passing the test; the test was created in PowerPoint-2007 with and ...

"Properties of inverse trigonometric functions" - Inverse trigonometric functions. Oral exercises. Let's solve the system of equations. Elective course in mathematics. Initial equation. Arc functions. Solve equations. Group work. Research. Repetition. Solving equations. Term. Calculate. Specify the scope of the function. Solution.

"Function y = cos x" - Y = k · cos x (properties). Y = - cos x. Increase, decrease. Y = cos (-x) (properties). Plotting the function y = cos x. Y = | cos x | (properties). Properties of the function y = cos x. Y = kcos x. Y = | cos x |. How to find the scope. Y = - cos x (properties). Function zeros, positive and negative values.

"Arcfunctions" - Arccos t. Y = arcctgx. Find the values ​​of the expressions. Function. Graphical method for solving equations. Expression. Equality. Inverse trigonometric functions. Domain. Trigonometric functions. Arccosx. Function definition area. Definitions. Range of values. Definition. Functional-graphic method for solving equations.

"Algebra" Trigonometric functions "" - Solving homogeneous trigonometric equations. Casting formulas. Converting sums of trigonometric functions into products. Transformation formulas for trigonometric functions. Formulas for converting a product of trigonometric functions into a sum. Homogeneous trigonometric equations. Sine and cosine.

"Convert trigonometric plots" - Parallel transfer. Stretching. Compression. Graph of the function y = f (| x |). Y = f (x). Part of the schedule. Cotangent function. Graph of the function y = | f (| x |) |. The characteristic of the graph of the harmonic oscillation. Plots of the resulting schedule. Graph of the function y = f (x). Conversion of graphs of trigonometric functions. Graph of the function y = | f (x) |.

"Functions of tangent and cotangent" - Function y = tgx. Solutions. Basic properties. Function properties. Building a graph. Schedule. Properties of the function y = tgx. y = ctgx. Equation roots. Numbers. The main properties of the function. Meaning. Function graph y = ctgx. Fraction.

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