求y=3tan(π/6-1/4)的周期及单调区间．
y=3tan(π/6-x/4)=-3tan(x/4-π/6)，所以T=π/|ω|=4π，所以y=3tan(π/6-x/4)的周期为4π；由kπ-π/2＜x/4-π/6＜kπ+π/2，得4kπ-4π/3＜x<4kπ+8π/3(k∈Z)，y=3tan(x/4-π/6)在(4kπ-4π/3，4kπ+8π/3)(k∈Z)内单调递增，所以y=3tan(π/6-x/4)在(4kπ-4π/3，4kπ+8π/3)(k∈Z)内单调递减．
求y=3tan(π/6-1/4)的周期及单调区间．
y=3tan(π/6-x/4)=-3tan(x/4-π/6)，所以T=π/|ω|=4π，所以y=3tan(π/6-x/4)的周期为4π；由kπ-π/2＜x/4-π/6＜kπ+π/2，得4kπ-4π/3＜x<4kπ+8π/3(k∈Z)，y=3tan(x/4-π/6)在(4kπ-4π/3，4kπ+8π/3)(k∈Z)内单调递增，所以y=3tan(π/6-x/4)在(4kπ-4π/3，4kπ+8π/3)(k∈Z)内单调递减．
