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Infringement complaint *Trigonometric function solving skills and formulas (sorted)*

On Several Solving Techniques About Trigonometric Functions

In more than ten years of vocational middle school mathematics teaching practice, I have accumulated some problem-solving skills, experience, and experience when facing the related teaching of trigonometric functions. Let ’s try to explore it: 1. Promotion and application of the relationship between sin cos and sin cos (or sin2):

2

1.Since (si cno) 2s si2 n co s 2si cno s1 2si cno s

, We must launch sin cos (or sin2), for example: (si nco) s

Example 1 Known sin cos

3

Find sin3 cos3. 3

Analysis: Since sin3 cos3 (sin cos) (sin2 sin cos cos2)

(sin cos) [(sin cos) 2 3sin cos]

Among them, sin cos is known, and only sin cos is required. This question is a typical knowledge of sin-cos. Find the type of sin cos.

Solution: ∵ (sin cos) 2 1 2sin cos Therefore: 1 2sin cos (

211) sin cos 333

sin3 cos3 (sin cos) [(sin cos) 2 3sin cos]

31314 [() 2 3] 333339

2. Application of the relationship between tg + ctg and sin ± cos, sin cos:

sin cos sin2 cos2 1

Since tg + ctg =

cos sin sin cos sin cos

Therefore: Knowing one of tg + ctg, sin cos, sin cos can infer the values of the remaining formulas.

Example 2 If sin + cos = m2 and tg + ctg = n, then the relationship of m2 n is ().

A. m2 = n B. m2 =

222

1 C. m2 D. n 2 nnm

Analysis: observe the relationship between sin + cos and sin cos:

(sin cos) 2 1m2 1

sin cos =

twenty two

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