f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三(1)化简f(x);(2)若 θ∈[0,π],求使f(x)成为偶函数的 θ取值;(3)在(2)成立的条件下,求满足f(x)=1,且x∈[-π,π]的x的集合.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/27 20:43:53
![f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三(1)化简f(x);(2)若 θ∈[0,π],求使f(x)成为偶函数的 θ取值;(3)在(2)成立的条件下,求满足f(x)=1,且x∈[-π,π]的x的集合.](/uploads/image/z/638062-70-2.jpg?t=f%28x%29%3D2sin%28x%2B+%CE%B8%2F2%29.cos%28x%2B+%CE%B8%2F2%29%2B2%E5%80%8D%E6%A0%B9%E5%8F%B7%E4%B8%89cos%26%23178%3B%28x%2B+%CE%B8%2F2%29-%E6%A0%B9%E5%8F%B7%E4%B8%89%EF%BC%881%EF%BC%89%E5%8C%96%E7%AE%80f%EF%BC%88x%EF%BC%89%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5+%CE%B8%E2%88%88%5B0%2C%CF%80%5D%2C%E6%B1%82%E4%BD%BFf%EF%BC%88x%EF%BC%89%E6%88%90%E4%B8%BA%E5%81%B6%E5%87%BD%E6%95%B0%E7%9A%84+%CE%B8%E5%8F%96%E5%80%BC%EF%BC%9B%EF%BC%883%EF%BC%89%E5%9C%A8%EF%BC%882%EF%BC%89%E6%88%90%E7%AB%8B%E7%9A%84%E6%9D%A1%E4%BB%B6%E4%B8%8B%2C%E6%B1%82%E6%BB%A1%E8%B6%B3f%EF%BC%88x%EF%BC%89%3D1%2C%E4%B8%94x%E2%88%88%5B-%CF%80%2C%CF%80%5D%E7%9A%84x%E7%9A%84%E9%9B%86%E5%90%88.)
x)KӨд5*ӨV8CHS/96zlΧ۟ʨ)[Xurtgu
i@^~l zѽQGGXgSc6n{ھ
g ?acsV@
*܅Ovo{d_l3PɎ) u7 ◳۞NгI*ҧ
/I@PSdXRSQ,ha0X]aA85!5T@Io$t fl\Vz[#*l
<(h,2>ph#HX&`䈀xԱ0Z,&tR:`F 1|Yn
f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三(1)化简f(x);(2)若 θ∈[0,π],求使f(x)成为偶函数的 θ取值;(3)在(2)成立的条件下,求满足f(x)=1,且x∈[-π,π]的x的集合.
f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三
(1)化简f(x);(2)若 θ∈[0,π],求使f(x)成为偶函数的 θ取值;(3)在(2)成立的条件下,求满足f(x)=1,且x∈[-π,π]的x的集合.
f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三(1)化简f(x);(2)若 θ∈[0,π],求使f(x)成为偶函数的 θ取值;(3)在(2)成立的条件下,求满足f(x)=1,且x∈[-π,π]的x的集合.
(1) f(x)=2sin(x+ θ/2).cos(x+ θ/2)+2倍根号三cos²(x+ θ/2)-根号三
=sin(2x+ θ)+√3[cos(2x+ θ)+1]-√3
=sin(2x+ θ)+√3[cos(2x+ θ)=2sin(2x+ θ+π/3)
(2) 若 θ∈[0,π],使f(x)成为偶函数
θ+π/3=π/2,θ=π/6
(3) f(x)=2sin(2x+ θ+π/3)=2sin(2x+π/6 +π/3)
=2cos2x=1
cos2x=1/2,2x=2kπ±π/3,
x=kπ±π/6,且,x∈[-π,π],
∴x=±π/6,x=±5π/6
x∈{-π/6,π/6,-5π/6,5π/6}