Question

使f(X)=SIN(2x+A)+(根号3)*COS(2X+A)为奇函数,

f(-π/4)=2 f(π/4)=-2
没明白

Answer 1

打错了
奇函数所以
f(-x)=-f(x)
半个周期递减 所以最大值在x= -π/4,函数最大值为2
那么f(π/4)=-f(-π/4)=-2

Answer 2

f(x)=
2
sin
(
2x
+
A
+
π/3
)f(-x)=-f(x)2
sin
(
-2x
+
A
+
π/3
)=
-
2
sin
(
2x
+
A
+
π/3
)-
sin
(
2x
-
A
-
π/3
)=
-
sin
(
2x
+
A
+
π/3
)
2x
-
A
-
π/3
+
2kπ
=
2x
+
A
+
π/3
A
=
Kπ
-
π/3
最小
正数
A
为
2π/3