"Trigonometric Identity Transformation" trigonometric functions PPT (sine, cosine and tangent formulas of the sum and difference of two angles in Lesson 3)

"Trigonometric Identity Transformation" trigonometric functions PPT (sine, cosine and tangent formulas of the sum and difference of two angles in Lesson 3)

Part One: Lecture, Practice and Interaction

Inverse use of trigonometric formulas

Evaluate: (1)sin π12-3cos π12;

(2)3-tan 15°1+3tan 15°.

Solving strategy

(1) When inverting the sine and cosine formulas of the sum and difference of two angles, you must first pay attention to whether the structure conforms to the characteristics of the formula, and secondly, pay attention to whether the angle meets the requirements.

(2) Pay attention to the application of special angles. When values ​​such as 12, 1, 32, 3, etc. appear in the formula, you must consider introducing special angles and construct the "value angle" into a form suitable for the formula.

Track training

1. The value of cos 24°cos 36°-cos 66°cos 54° is equal to ()

A． 0B. 12

C． 32D. -12

2. It is known that sin α+cosα-π6=435, then the value of sinα+7π6 is ________.

3. Assume a=sin 14°+cos 14°, b=sin 16°+cos 16°, then the size relationship between a and b is ________ (connect with "<").

How to use trigonometric formulas

Calculation: (1)tan π9＋tan 2π9＋3tan π9tan 2π9;

(2)(1＋tan 21°)(1＋tan 22°)(1＋tan 23°)(1＋tan 24°).

Solving strategy

Deformation conclusion of tangent function formula

tan(α+β)(1-tan αtan β)=tan α+tan β;

tan α＋tan β＋tan αtan βtan(α+β)=tan(α+β);

tan α-tan β=tan(α-β)•(1+tan αtan β);

tan α-tan β-tan αtan βtan(α-β)=tan(α-β)．

Simplification of trigonometric functions

Simplify: (1)(tan 10°-3)•cos 10°sin 50°;

(2)sin(α+β)cos α-12[sin(2α+β)-sin β].

Solving strategy

The formula of a trigonometric function simply follows the "three looks" principle, that is, look at the angle first, look at the name, and thirdly look at the structure and characteristics of the formula.

(1) Look at the characteristics of angles, make full use of the relationship between angles, try to transform them into the same angle, and use known angles to construct the angle to be found;

(2) Look at the characteristics of the function name, transform it into a function with the same name, and make it interactive;

(3) Look at the structural characteristics of the formulas, start from the overall perspective, and use these formulas in forward, reverse, and deformed ways.

Trigonometric Identity Transformation PPT, Part 2: Feedback on Compliance

1. sin 20°cos 10°－cos 160°sin 10°＝()

A． -32B. 32

C． -12 D． 12

2. In △ABC, C=120°, tan A+tan B=233, then the value of tan Atan B is ________.

3. It is known that sin(α-β)cos α-cos(β-α)sin α=45, β is the third quadrant angle, find the value of sin(β+π4).

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