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1奇偶性求f(x)=Asin(ωx+φ)奇偶性的方法较多,如定义法、特殊值法等。但笔者认为,用下列结论解此类问题能给学生提供一个基本的解法。结论:(1)y=Asinωx(A≠0,ω≠0)是奇函数。(2)y=Acosωx(A≠0,ω≠0)是偶函数。(3)设f(x)=Asin(ωx+φ)(A≠0,ω≠0),当φ=kπ(k∈Z)时,f(x)是奇函数;当φ=kπ+π/2(k∈Z)时,f(x)是偶函数;当φ≠(kπ)/2(k∈Z)时,f(x)是非奇非偶的函数。(4)设f(x)=Acos(ωx+φ)(A≠0,φ≠0),当φ=kπ(k∈Z)时,f(x)是偶函数;当φ=kπ+π/2(k∈Z)
1 parity Find f (x) = Asin (ωx + φ) more methods of parity, such as the definition of law, special value method. However, I believe that using the following conclusions to solve such problems give students a basic solution. Conclusion: (1) y = Asinωx (A ≠ 0, ω ≠ 0) is an odd function. (2) y = Acosωx (A ≠ 0, ω ≠ 0) is an even function. (3) Let f (x) = Asin (ωx + φ) (A ≠ 0, ω ≠ 0), and f (x) is an odd function when φ = kπ / 2 (k ∈ Z), f (x) is an even function and f (x) is a non-odd function when φ ≠ (kπ) / 2 (k ∈ Z). (4) Let f (x) = Acos (ωx + φ) (A ≠ 0, φ ≠ 0). When φ = kπ / 2 (k∈Z)