广义勾股定理和广义三角函数

The Generalized Pythagorean Theorem and the Generalized Trigonometric Function

众所周知,只有直角三角形才有勾股定理,把勾股定理推广到除等边三角形以外的任意三角形,引入广义勾股定理,根据广义勾股定理,广义三角函数,得到解三角形的简捷方法广义三角函数跟正弦函数余弦函数一样,都是周期函数,单调性也相同,图像也差不多,而且还具备正弦函数余弦函数不具备的许多优点,因此建议把它看成基本初等函数并取代正弦函数余弦函数。广义三角函数在物理学以及其他学科中都有重要应用,例如在水波、声波、简谐振动和交流电中,这些问题用广义三角函数研究比纯粹用三角函数研究更精确更好。广义勾股定理是勾股定理的推广,具有重要的理论和应用价值。

It is well known that only right triangle has Pythagorean theorem.The Pythagorean theorem is extended to any triangle except equilateral triangle,introduce the generalized Pythagorean theorem and the generalized trigonometric function,a simple method to solve a triangle is obtained,so that the sine theorem cosine theorem is no longer needed to solve the triangle.The generalized trigonometric function is a periodic function and has the same monotonicity,similar image with the trigonometric function.The generalized trigonometric function has important applications in physics and other subjects,such as water wave,sound wave,simple harmonic vibration and alternating current.