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我们知道,应用反三角函数表示角是很方便的。但由于特定条件下的角其范围与反三角函数的值域往往不一致,在应用反三角函数表示这些角时,就要进行换算,否则,会发生错误。本文对应用反三角函数表示直线的倾斜角、复数辐角主值及把形如asinx+bcosx的表达式化为含一个三角函数的表达式时的辅助角的选取等问题进行探讨,从而得到相应的选取原则。先看一个例题。例1 直线2x+y+3=0的倾斜角等于( )。 (A)arctg2。(B)arctg(-2)
We know that it is very convenient to use an inverse trigonometric function to represent the angle. However, because the range of angles and the range of inverse trigonometric functions are often inconsistent under certain conditions, when these angles are represented by an inverse trigonometric function, scaling is performed. Otherwise, an error occurs. This paper discusses the application of inverse trigonometric functions to represent the inclination angle of a straight line, the principal values of complex angles, and the selection of an auxiliary angle when an expression such as asinx+bcosx is converted into an expression containing a trigonometric function. The selection principle. Look at an example first. Example 1 The inclination of the line 2x+y+3=0 is equal to (). (A) arctg2. (B) arctg (-2)