论文部分内容阅读
三角变换往往包含不同名的三角函数、不同类的角和不同结构的式子,所以通常比代数变换更复杂.也正因为此,三角变换比代数变换更具多样性,方法更灵活,思路更开阔.这其中有两个原则是做三角变换问题时不能忘却的;“化繁为简”和“消除差异”. 一、化繁为简 三角变换中的化繁为简是指:化复角为单角;化不同角为同角;化不同名函数为同名函数;化高次为低次;化多项式为单项式;化无理式为有理式,化分式为整式等. 例1 求cos40°+cot80°的值. 分析所给式子的两项的函数名称和角都不同,所以可以从名称上突破,也可以从角突破.若从名称入手,应把不熟悉的余割、余切化归为较熟悉的正弦、余弦来处理;若从角入手,则40°十80°=120°,可考虑互化两角.
Trigonometric transforms often contain differently named trigonometric functions, different types of angles, and different structural equations, so they are usually more complex than algebraic transforms. Because of this, trigonometric transforms are more versatile than algebraic transforms, and methods are more flexible. Openness. There are two principles that can not be forgotten when doing the triangular transformation problem; “reducing complexities and simplifying” and “eliminating differences.” 1. Familiarity with simplicity Familiarization with simplicity in triangular transformation refers to: complex angle For single angles; for different angles for the same angle; for the different name function for the function of the same name; high-order low-order; chemical polynomial for single-term; chemical and irrational for rational, divided fractions for the whole and so on. Example 1 find cos40 ° + cot 80 ° value. The analysis of the formula for the two items of the function name and angle are different, so you can break from the name, you can also break from the corner. If you start from the name, you should not familiar with the co-cut, co-cut Into the more familiar sine, cosine to deal with; if starting from the corner, then 40 ° X 80 ° = 120 °, can consider two angles.