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由直线倾斜角的取值范围求直线斜率的取值范围或由直线斜率的取值范围求直线的倾斜角的取值范围时,一定要注意运用正切函数在[0,π)上的图像,借助正切函数的单调性来求解。这时要特别注意k=tanα在[0,π)上不是单调的,当k>0时,倾斜角为锐角;当k<0时,倾斜角为钝角;k不存在时,倾斜角为90°;反之亦然,特别地,当斜率k有正也有负时,倾斜角有锐角和钝角两部分。
When calculating the range of the straight line slope from the range of the straight line inclination angle or the range of the straight line inclination angle from the range of the straight line slope, pay attention to using the image with the tangent function at [0, π) Solve with the monotonicity of a tangent function. In this case, special attention should be paid to the fact that k = tanα is not monotonous on [0, π) and is acute when k> 0 and obtuse when k <0; ° and vice versa. In particular, when the slope k is positive and negative, the inclination angle has two parts, an acute angle and an obtuse angle.