均值不等式是求代数最值的重要方法,而且过程简单,应用广泛,如果把它迁移到三角函数中,还能求三角函数的最值,解这类题不仅满足一正、二定、三相等的要求,还要根据三角函数的特点作技巧性的变形,现举例说明.例1求函数y=4sin~2θ+csc~2θ的最小值.分析注意到正弦函数sinθ与余割函数cscθ互为倒数,易求y的最小值.解∵y=4sin~2θ+csc~2θ≥2·2sinθ·cscθ=4,∴y_(最小)=4.点评运用不等式求最值应注意放缩的合理性,并判断等号是否可取.对等号不可取 Mean inequality is an important method to find the most value of algebra. The process is simple and has a wide range of applications. If you move it to a trigonometric function, you can find the most value of the trigonometric function. Solving such problems not only satisfies one positive, two definite, three equal , But also according to the characteristics of trigonometric functions for technical deformation, are an example of Example 1. Seeking the minimum value of the function y = 4sin ~ 2θ + csc ~ 2θ. Analysis noted that the sine function cotθ and cosine cscθ each other Reciprocal, easy to find the minimum value of y. Solution ∵y = 4sin ~ 2θ + csc ~ 2θ≥2 · 2sinθ · cscθ = 4, ∴y_ (min) = 4. Comments The use of inequality for the maximum value should be noted that the rationality of scaling , And determine whether the equal sign is desirable. Equal sign is not desirable