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三角函数(在相应区间内)的单调性,和三角函数的其他性质(奇偶性,有界性,周期性等)一样,是三角函数的基本性质之一,它也是学习反三角函数,解三角不等式,确定某些函数的定义域,绘制三角函数图象的理论根据。但学生对三角函数的单调性及相应的单调区间,往往理解的并不清楚。“正切是永远上升的”,“余切是永远下降的”这种不正确的说法,就是不理解正切(余切)的单调性的反映。事实上正切在整个定义域内是没有单调性可言的,比如:0°<45°<135°,tg0°tg135°,这对单调函数来说
The monotonicity of the trigonometric function (in the corresponding interval), as well as the other properties of the trigonometric function (parity, boundedness, periodicity, etc.), is one of the basic properties of the trigonometric function. It is also a learning inverse trigonometric function, solving triangles. Inequality, defining the domain of some functions, and drawing the theoretical basis of trigonometric functions. However, students often do not understand the monotonicity of the trigonometric function and the corresponding monotonous interval. “The tangent is always on the rise,” and the inaccurate statement that “the cognac is forever decreasing” is that it does not understand the monotonous reflection of the tangent (coalesal). In fact the tangent is not monotonic at all in the entire definition domain, such as: 0°<45°<135°, tg0°tg135°, which is a monotonic function