"Graphics and Properties of Trigonometric Functions" Trigonometric Functions PPT (Graphics of sine functions and cosine functions in the first lesson)

"Graphics and Properties of Trigonometric Functions" Trigonometric Functions PPT (Graphics of sine functions and cosine functions in the first lesson)

Part One: Learning Objectives

Understand how to use sine lines to create the graph of the sine function,

Be able to use the "five-point method" to draw the graphs of sine and cosine functions

Able to use graphics of sine and cosine functions to solve simple problems

PPT on the images and properties of trigonometric functions, part 2: independent learning

Problem guide

Preview textbooks P196-P200 and think about the following questions:

1. How to transform the image of y=sin x, x∈0,2π into the image of y=sin x, x∈R?

2. What are the five key points of the graphs of sine and cosine functions?

A preliminary exploration of new knowledge

Graphs of sine function and cosine function

■Instructions from famous teachers

The "five points" in the "five-point method" drawing refer to the highest and lowest points of the sine and cosine functions as well as the intersection points of the image and the coordinate axis. This is the most commonly used method to draw graphs of sine functions and cosine functions.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) The graph of the function y=sin x is translated to the right by π2 units to obtain the graph of the function y=cos x. ()

(2) The graph of function y=cos x is symmetrical about the x-axis. ()

(3) The shape of the graph of the function y = sin x, x∈ 0, 2π is completely consistent with the shape of the graph of the function y = cos x, ． ()

When using the "five-point method" to draw the image of y=sin x, x∈[0,2π], the following points are not key points: ()

A． π6,12B. π2,1

C． (π,0) D. (2π,0)

Function y=cos x, an axis of symmetry of the x∈R graph is ()

A． x-axis B． y-axis

C． Line x=π2 D. Line x=3π2

Graphics and properties of trigonometric functions PPT, the third part: interactive lecture and practice

Use the "five-point method" to draw graphs of trigonometric functions

Use the "five-point method" to make a simplified diagram of the following function:

(1)y=12+sin x, x∈[0, 2π];

(2)y=1-cos x, x∈[0, 2π].

Interactive exploration

1. (Variable conditions) If "x∈[0, 2π]" in this example (1) is changed to "x∈-5π6, 7π6", how to draw the function graph.

2. (Variable conditions) If the "function y=1-cos x" in this example (2) is replaced by "y=1-sin x", what will the image look like?

regular method

Three steps to use trigonometric function graphics to solve sin x>a (or cos x>a)

(1) Make the image of y=a, y=sin x (or y=cos x).

(2) Determine the x value of sin x=a (or cos x=a).

(3) Determine the solution set of sin x>a (or cos x>a).

[Note] To solve the trigonometric inequality sin x>a, if the range is not limited, generally use the image to find the value range of x within the range of Then based on the fact that the values ​​of the same trigonometric functions with the same terminal sides and angles are equal, write the solution set of the original inequality.

Graphics and Properties of Trigonometric Functions PPT, Part 4: Feedback on Compliance

1. The simplified diagram of function y=sin(-x), x∈[0, 2π] is ()

2. To get the image of y=cos x, x∈�-2π,0�, just change the image of y=cos _Translation________ unit length.

3. Use the "five-point method" to draw the graph of the function y=sinx-π2x∈π2,5π2.

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For more information about the PPT courseware "Graphics and Properties of Trigonometric Functions, Graphics of Sine Functions and Cosine Functions", please click on the ppt tag of "Graphics and Properties of Trigonometric Functions ppt Sine Function and Cosine Functions".

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