三角题常常涉及到角的范围问题,稍不留意,就会失误,因此在三角学习中,要重视对角的范围的讨论。一、挖掘隐含条件,明确角的范围有时已知条件没有直接告诉角的范围,需要认真分析已知条件,进行综合推理,得出角的范围。例1 如果θ是第二象限角,且 cos(θ/2)-sin(θ/2)=(1-sinθ)~(1/2),那么θ/2是第几象限的角? 解∵2kπ+π/2<θ<π+2kπ(k∈Z), ∴kπ+π/4<θ/2<π/2+kπ。即2nπ+π/4<π/2+2+2nπ(n∈Z) 或2nπ+5π/4<θ/2<3π/2+2nπ (1) 又cos(θ/2)-sin(θ/2)=(1-sinθ)(1/2)即cos(θ/2)-sin(θ/2)=|cos(θ/2)-sin(θ/2)|, Trigonometry questions often involve the range of angles. If you do not pay attention, you will make mistakes. Therefore, in the study of triangles, you should pay attention to the discussion of the scope of the angle. First, excavate implicit conditions, clear the scope of the angle sometimes known conditions do not directly tell the scope of the angle, need to carefully analyze the known conditions, conduct comprehensive reasoning, come to the scope of the angle. Example 1 If θ is the second quadrant angle, and cos(θ/2)-sin(θ/2)=(1-sinθ) ((1/2), then θ/2 is the angle of the fourth quadrant? 2kπ+π/2<θ<π+2kπ(k∈Z), ∴kπ+π/4<θ/2<π/2+kπ. That is, 2nπ+π/4<π/2+2+2nπ(n∈Z) or 2nπ+5π/4<θ/2<3π/2+2nπ (1) and cos(θ/2)-sin(θ/ 2)=(1-sinθ)(1/2) that is cos(θ/2)-sin(θ/2)=|cos(θ/2)-sin(θ/2)|,