在直角坐标系xoy中,各象限的角平分线连同轴、y轴共八条射线,它们把直角坐标系分成八个区域,在各射线上标上相应的sinα+cosα的值,就可以很方便地判断出α的范围。如上图建立坐标系,设sinα+cosα=x,且α∈〔02π〕,A(1,1).〔结论1〕若1x≤2√,则α∈〔0,π/2〕.证明:∵sinα In the orthogonal coordinate system xoy, the angle bisectors of each quadrant together with the axis and y-axis have eight rays. They divide the rectangular coordinate system into eight regions, and the corresponding sinα+cosα values ​​are marked on each ray. The range of α is conveniently judged. The above figure establishes a coordinate system, set sinα+cosα=x, and α∈[02π], A(1,1). [Conclusion 1] If 1x≤2√, then α∈[0,π/2]. Proof: ∵sinα