求函数y=cosx+cos(x-π3)(x∈R)的最大值和最小值.
问题描述:
求函数y=cosx+cos(x-
)(x∈R)的最大值和最小值. π 3
答
∵y=cosx+cos(x-
)π 3
=cosx+cosxcos
+sinxsinπ 3
π 3
=
cosx+3 2
sinx
3
2
=
(cos
3
cosx+sinπ 6
sinx)π 6
=
cos(x-
3
),π 6
∵-1≤cos(x-
)≤1,π 6
∴ymax=
,ymin=-
3
.
3