"Induced Formula" Trigonometric Function PPT (Induced Formula Five and Six in Lesson 2)

Description

"Induced Formula" Trigonometric Function PPT (Induced Formula Five and Six in Lesson 2)

Part One: Learning Objectives

Master the derivation process of induction formulas 5 and 6

Able to use induced formulas to solve simple evaluation, simplification and proof problems

Induction formula PPT, part 2 content: independent learning

Problem guide

Preview textbooks P191-P193 and think about the following questions:

1.What is the symmetrical relationship between the terminal side of π2-α and the terminal side of α?

2. What are the contents of induction formulas 5 and 6?

A preliminary exploration of new knowledge

1. Formulas five and six

2. Linguistic summary of formulas five and six

The sine (cosine) function values ​​of π2±α are respectively equal to the _______________ function values ​​of α, preceded by a symbol that represents the original function value when α is regarded as _______.

Formulas 1 to 6 are all called induction formulas.

■Instructions from famous teachers

Induction formulas 5 and 6 reflect the relationship between the trigonometric function values ​​of angle π2±α and α. You can use the formula "change the function name, look at the quadrant for the symbol" to memorize it.

self-test

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

(1) The angle α in the induction formulas 5 and 6 can only be acute angles. ()

(2)sinα-π2=cos α.()

(3) If α is the second quadrant angle, then sinπ2+α=cos α.()

It is known that sin α=23, then cosπ2-α is equal to ()

A． 23B. -twenty three

C． 53D． -53

It is known that sin(α+π2)=13, α∈(-π2, 0), then sin α is equal to ()

A． -225 B.225

C． -223 D.223

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

Use the induction formula to evaluate

(1) It is known that cos(π+α)=-12, α is the first quadrant angle, find the value of cosπ2+α.

(2) Given that sinπ3-α=12, find the value of cosπ6+α.

regular method

To answer such questions, you must learn to discover their mutual complementarity: such as π3-α and π6+α, π3+α and π6-α, π4-α and π4+α, etc., π3+θ and 2π3-θ, π4+θ and 3π4-θ, etc. , when encountering this kind of problem, you might as well consider the sum of two angles, and be good at using angle transformation to solve the problem.

Use induced formulas to simplify and prove

Simplify: cos3π2-α•sinπ2-α•sinπ2+αcos5π2-α•sin-3π2-α.

regular method

(1) Steps to use induced formulas to simplify trigonometric function expressions

The trigonometric function of any angle can be converted into an acute angle trigonometric function by using the induction formula, that is, the formula is: "convert negative to positive, large to small, and then look up the table after changing to an acute angle."

(2) Common methods for proving trigonometric identities

① Pushing from the left to the right or from the right to the left follows the principle of simplifying the complex; ② Prove that the left side = A and the right side = A, then the left side = the right side, and A here plays the role of a bridge; ③ By doing Difference or quotient proof, that is, left side - right side = 0 or left side right side = 1 or right side left side = 1.

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

1. If sinπ2+θ<0, and cosπ2-θ>0, then θ is ()

A． First quadrant angle B. second quadrant angle

C． Third quadrant angle D. Fourth quadrant angle

2. If sin(3π+α)=-12, then cos7π2-α is equal to ()

A． -12 B． 12

C． 32 D. -32

3. Simplify: sinπ2+αcosπ2-αcos(π+α)+sin(π-α)cosπ2+αsin(π+α)

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Update Time: 2024-09-11

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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