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

"Function y \u003d cos x" - Zeros of the function, positive and negative values. Let's find some points for plotting. Y \u003d cos (x - a). Transforming the graph of the function y \u003d cos x. Function y \u003d cos x. Y \u003d 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 \u200b\u200bof the function. Solve equations. Find the meaning of the expression. Solving equations. Working in groups. Elective course in mathematics. Arc functions. Let's solve the system of equations. Research. Specify the scope of the function. Reiteration. The triple satisfies the original equation.

"Functions of tangent and cotangent" - Properties of the function y \u003d tgx. Solutions. Equation roots. Schedule. Building a graph. Function properties. Value. Fraction. Basic properties of the function. Function y \u003d tgx. Basic properties. y \u003d ctgx. Function graph y \u003d ctgx. Numbers.

"Convert trigonometric graphs" - Sine function. Convert graphs of trigonometric functions. Characteristic of the harmonic oscillation graph. Graph of the function y \u003d f (x) + m. Cosine function. Graph of the function y \u003d f (| x |). Graph of the function y \u003d | f (x) |. Characteristic of transformations of graphs of functions. Y \u003d 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 \u003d arcctgx. Arcctg t \u003d 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 \u200b\u200bof trigonometric functions of some angles. A guide to algebra and the principles 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 function y \u003d sinx Graph of function y \u003d sinx Properties of function y \u003d sinx Properties of function y \u003d sinx Graph of function y \u003d cosx Graph function y \u003d cosx Properties of function y \u003d cosx Properties of function y \u003d cosx Comparison of properties of functions y \u003d sinx and y \u003d cosx Comparison of properties of functions y \u003d sinx and y \u003d cosx

Properties of the function y \u003d sinx 6. Intervals of constant sign of the function y \u003d sinx: sinx\u003e 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 \u003d "(! LANG: Properties of the function y \u003d sinx 6. Sign intervals of the function y \u003d sinx: sinx\u003e 0 for x (2k; + 2k), sinx

Properties of the function y \u003d cosx 6. Intervals of constant sign of the function y \u003d cosx: cosx\u003e 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 \u003d "(! LANG: Properties of the function y \u003d cosx 6. Intervals of constant sign of the function y \u003d cosx: cosx\u003e 0 for x (- / 2 + k; / 2 + k), k cosx

Comparison of the properties of functions y \u003d sinx and y \u003d cosx Function y \u003d sinxy \u003d cosx Domain D (sinx) \u003d D (cosx) \u003d Set of values \u200b\u200bE (sinx) \u003d [-1,1] E (cosx) \u003d [-1,1] Parity and odd odd even Zeros of the function x \u003d k, kx \u003d / 2 + k, k Intervals of constant sign y (x)\u003e 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 \u003d sin x, its properties and graph. Lesson objectives: To review and systematize the properties of the function y \u003d sin x. Learn to plot the function y \u003d sin x.

y \u003d sin x Domain of definition - the set R of all real numbers: D (f) \u003d (- ∞; + ∞) Property 1.

y \u003d sin x Since sin (-x) \u003d - sin x, then y \u003d sin x is an odd function, which means its graph is symmetric about the origin. Property 2.

y \u003d sin x The function y \u003d increases on the segment and decreases on the segment [π / 2; π]. Property 3.0 π / 2 π

y \u003d sin x The function y \u003d sin x is bounded both from below and from above: - 1 ≤ sin x ≤ 1 Property 4.

y \u003d sin x y naim \u003d -1 y naib \u003d 1 Property 5. 0 π / 2 π

Let us plot the function y \u003d 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 \u003d 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. Working in groups. Research. Reiteration. Solving equations. Term. Calculate. Specify the scope of the function. Decision.

"Function y \u003d cos x" - Y \u003d k · cos x (properties). Y \u003d - cos x. Increase, decrease. Y \u003d cos (-x) (properties). Plotting the function y \u003d cos x. Y \u003d | cos x | (properties). Properties of the function y \u003d cos x. Y \u003d k cos x. Y \u003d | cos x |. How to find the scope. Y \u003d - cos x (properties). Function zeros, positive and negative values.

"Arcfunctions" - Arccos t. Y \u003d arcctgx. Find the values \u200b\u200bof 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.

"Converting trigonometric graphs" - Parallel transfer. Stretching. Compression. Graph of the function y \u003d f (| x |). Y \u003d f (x). Part of the schedule. Cotangent function. Graph of the function y \u003d | f (| x |) |. Characteristic of the harmonic oscillation graph. Plots of the resulting schedule. Graph of the function y \u003d f (x). Convert graphs of trigonometric functions. Graph of the function y \u003d | f (x) |.

"Functions of tangent and cotangent" - Function y \u003d tgx. Solutions. Basic properties. Function properties. Building a graph. Schedule. Properties of the function y \u003d tgx. y \u003d ctgx. Equation roots. Numbers. Basic properties of the function. Value. Function graph y \u003d ctgx. Fraction.

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