题目
已知函数f(x)=2sin(x-
π |
6 |
提问时间:2021-04-01
答案
(Ⅰ)f(x)=2sin(x-
)sin[
+(x-
)]=2sin(x-
)cos(x-
)=sin(2x-
),
∵ω=2,∴函数f(x)的最小正周期T=
=π;
(Ⅱ)由(Ⅰ)得,f(
+
)=sin[2(
+
)-
]=sinC,
由已知sinC=
,
又角C为锐角,
∴C=
,
∵A=
,
∴由正弦定理
=
,得
=
=
π |
6 |
π |
2 |
π |
6 |
π |
6 |
π |
6 |
π |
3 |
∵ω=2,∴函数f(x)的最小正周期T=
2π |
2 |
(Ⅱ)由(Ⅰ)得,f(
C |
2 |
π |
6 |
C |
2 |
π |
6 |
π |
3 |
由已知sinC=
1 |
2 |
又角C为锐角,
∴C=
π |
6 |
∵A=
π |
4 |
∴由正弦定理
BC |
sinA |
AB |
sinC |
BC |
AB |
sinA |
sinC |
|