方程cos^2-sin^2+sinx=m+1有实数解 求实数m的取值范围

问题描述:

方程cos^2-sin^2+sinx=m+1有实数解 求实数m的取值范围

解题思路将cos^2换成1-sin^2然后求等式右边的值域结果m属于闭区间9/8,43/16

cos²x-sin²x+sinx=m+11-2sin²x+sinx=m+1m=-2sin²x+sinx=-2(sinx-1/4)²+1/8-1≤sinx≤1 -5/4≤sinx-1/4≤3/4 0≤(sinx-1/4)²≤25/16 -25/8≤-2(sinx-1/4)²≤0-25/8+1/8≤-2(sinx-...