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# Trigonometric function solving skills and formulas (sorted)

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