函数f(x)=sin(2x+ф).(-π＜ф＜0).图像一条对称轴是x=π/8.(1)求ф值(2)求tan(ф+π/3)

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函数f(x)=sin(2x+ф).(-π＜ф＜0).图像一条对称轴是x=π/8.
(1)求ф值
(2)求tan(ф+π/3)

sin的对称轴即取最值的地方
所以sin(2π/8+ф)=±1
π/4+ф=kπ+π/2
ф=kπ+π/4
所以k=-1
ф=-3π/4
tan(-3π/4)=-1,tanπ/3=√3
tan(ф+π/3)
=[tan(-3π/4)+tanπ/3]/[1-tan(-3π/4)tanπ/3]
=2-√3

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