"Induced Formula" Trigonometric Functions PPT (Induced Formulas 2, 3, and 4 in Lesson 1)

Description

"Induced Formula" Trigonometric Functions PPT (Induced Formulas 2, 3, and 4 in Lesson 1)

Part One: Learning Objectives

Understand how to derive induction formulas

Able to use formulas to evaluate, simplify and prove trigonometric functions.

Induction formula PPT, part 2 content: independent learning

Problem guide

Preview the textbook P188-P190 and think about the following questions:

1. π±α, what is the symmetrical relationship between the terminal side of -α and the terminal side of α?

2. What are the contents of induction formulas 2, 3 and 4?

A preliminary exploration of new knowledge

1.Formula 2

The terminal sides of angle π+α and angle α are symmetric about _________

formula

sin(π+α)=__________,

cos(π+α)=___________,

tan(π+α)＝__________

2.Formula 3

Angle -α and the terminal side of angle α are symmetrical about _______

formula

sin(-α)=___________,

cos(-α)=___________,

tan(-α)＝-tan α

3. Formula 4

The terminal sides of angle π-α and angle α are symmetric about _____

formula

sin(π-α)=__________,

cos(π-α)=__________,

tan(π-α)＝__________

■Instructions from famous teachers

Inducing formula memory

(1) Memory method: The trigonometric function value of 2kπ+α, -α, π±α is equal to the function value of α with the same name, preceded by a symbol that represents the original function value when α is regarded as an acute angle.

(2) Memory tip: "The function name remains unchanged, and the symbols look at the quadrants."

The correct understanding of the "mantra": "the function name remains unchanged" means that the trigonometric functions on both sides of the equation have the same name; "sign" refers to whether the right side of the equal sign is a positive or negative sign; "looking at the quadrant" means assuming that α is an acute angle, depending on the In this formula, whether the original function name takes a positive value or a negative value in the quadrant where the terminal side of the angle is located, such as sin(π+α), if α is regarded as an acute angle, then π+α is in the third quadrant, and sine takes a negative value in the third quadrant, so sin(π+α)=-sin α.

self-test

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

(1) The induced formula 3 can convert the trigonometric function value of any negative angle into the trigonometric function value of a positive angle. ()

(2) The angle α in the induction formula must be an acute angle. ()

(3) From the induction formula three, we know that cos[-(α-β)]=-cos(α-β). ()

(4) In △ABC, sin(A+B)=sin C． ()

Which of the following formulas is correct ()

A． sin(π-α)=-sin α

B. cos(π+α)＝cos α

C． cos α=sin α

D. sin(2π+α)=sin α

Inducement formula PPT, the third part: lecture and practice interaction

Angle evaluation problem

Use the formula to find the values ​​of the following trigonometric functions:

(1)cos 476π; (2)tan(-855°);

(3)sin(-945°)+cos(-296π);

(4)tan 34π＋sin 116π.

Track training

1. (2019•Chongqing First Intermediate Final Test)tan5π3=()

A． -3B. 3

C． -33 D. 33

2. Find the values ​​of each of the following trigonometric functions:

(1)cos-31π6;

(2)tan(-765°);

(3)sin 4π3·cos 25π6·tan 5π4.

Simplify the evaluation problem

Simplify the following expressions.

(1)tan(2π-α)sin(-2π-α)cos(6π-α)cos(α-π)sin(5π-α);

(2)sin(1 440°+α)•cos(α-1 080°)cos(-180°-α)•sin(-α-180°).

regular method

Common methods for simplifying trigonometric functions

(1) Use the induction formula to convert the trigonometric function of any angle into the trigonometric function of an acute angle.

(2) Tangential chord transformation: Generally, the tangent function in the expression needs to be converted into a chord function.

(3) Pay attention to the application of “1”: 1=sin2α＋cos2α=tan π4.

Induction formula PPT, the fourth part: feedback on meeting standards

1. Calculate cos(-600°)=()

A.32B.－32

C.12 D.－12

2. It is known that cos(α-π)=-513, and α is the fourth quadrant angle, then sin(-2π+α) is equal to ()

A． -1213 B． 1213

C． ±1213 D. 512

3. Calculate tan 690° = ________.

4. Simplify: sin(540°+α)•cos(-α)tan(α-180°).

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Update Time: 2024-10-02

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