问题
解答题
已知函数f(x)=cos(x-
(Ⅰ)若f(α)=
(II)设g(x)=f(x)•f(x+
|
答案
(Ⅰ)∵f(α)=cos(α-
π |
4 |
7
| ||
10 |
∴
| ||
2 |
7
| ||
10 |
7 |
5 |
两边平方得,sin2α+2sinαcosα+cos2α=
49 |
25 |
即1+sin2α=
49 |
25 |
24 |
25 |
(II)g(x)=f(x)•f(x+
π |
2 |
π |
4 |
π |
4 |
=
| ||
2 |
| ||
2 |
=
1 |
2 |
1 |
2 |
当x∈[-
π |
6 |
π |
3 |
π |
3 |
2π |
3 |
所以,当x=0时,g(x)的最大值为
1 |
2 |
π |
3 |
1 |
4 |
即函数g(x)在区间[-
π |
6 |
π |
3 |
1 |
2 |
π |
3 |
1 |
4 |