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正弦和余弦函数的有界性是指|sinx|≤1(A)和|cosa|≤1(B)在中数教学中有时利用正、余弦函数的这个性质来研究问题可化繁为简,化难为易,它不仅在三角中,而且在其他中学数学课程中都有广泛的应用。本文将利用正、余弦函数的有界性解决如下几个方面的问题。一、利用正、余弦函数的有界性求值例1 已知|sinx|-3cosy=4,求x、y。此题已知条件是含有两个变量x、y的等式,利用三角恒等变形来求解是比较困难的;如果考虑性质(A)、(B),可大大减少计算量,从而可迅速准确的获解。解由原等式得3cosy=|sinx|-4≤1-4=-3∴cos≤-1又cosy≥-1,故cosy=-1,于是|sinx|=1 故
The boundedness of the sine and cosine functions means that |sinx| ≤1(A) and |cosa|≤1(B) sometimes use the properties of the positive and cosine functions to study problems in medium-numeric teaching. It is difficult to change. It is widely used not only in the triangle but also in other middle school mathematics courses. This article will use the boundedness of the positive and cosine functions to solve the following problems. First, the use of positive and cosine function of the boundedness evaluation Example 1 |sinx|-3cosy=4 is known, find x, y. The known condition of this problem is an equation containing two variables x and y. It is difficult to solve using trigonometric constant deformation; if the properties (A) and (B) are taken into consideration, the amount of calculation can be greatly reduced, and thus, it can be quickly and accurately. The settlement. Solution by the original equation 3cosy = | sinx | -4 ≤ 1-4 = -3 ∴ cos ≤ -1 and cosy ≥ -1, so cos == 1, so | sinx | =1