三角函数的概念。图像和性质。群力考卷
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/10 22:21:13
大题求解。精简下。。麻烦速度下喔。。
![](http://img.wesiedu.com/upload/5/7b/57b6df6b249503cb2b220a7387c46009.jpg)
![](http://img.wesiedu.com/upload/5/7b/57b6df6b249503cb2b220a7387c46009.jpg)
![三角函数的概念。图像和性质。群力考卷](/uploads/image/z/19419954-42-4.jpg?t=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E6%A6%82%E5%BF%B5%E3%80%82%E5%9B%BE%E5%83%8F%E5%92%8C%E6%80%A7%E8%B4%A8%E3%80%82%E7%BE%A4%E5%8A%9B%E8%80%83%E5%8D%B7)
解题思路: 考查三角函数的性质
解题过程:
解:∵f(0)=f(2π/3) ,即sin2π/3(acos2π/3+sin2π/3)=0
解得:a=根号3
∴f(x)=sinx(根号3cosx+sinx)=根号3/2sin2x+1/2(1-cos2x)
=根号3/2sin2x-1/2cos2x+1/2=sin(2x+π/6)+1/2
∵x∈[5π/24,π/2] ∴2x+π/6∈[π/4, 5π/6]
当2x+π/6=π/2时,f(x)取最大值,最大值为3/2,此时x=π/6;
当2x+π/6=5π/6时,f(x)取最小值,最小值为1,此时x=π/3
最终答案:略
解题过程:
解:∵f(0)=f(2π/3) ,即sin2π/3(acos2π/3+sin2π/3)=0
解得:a=根号3
∴f(x)=sinx(根号3cosx+sinx)=根号3/2sin2x+1/2(1-cos2x)
=根号3/2sin2x-1/2cos2x+1/2=sin(2x+π/6)+1/2
∵x∈[5π/24,π/2] ∴2x+π/6∈[π/4, 5π/6]
当2x+π/6=π/2时,f(x)取最大值,最大值为3/2,此时x=π/6;
当2x+π/6=5π/6时,f(x)取最小值,最小值为1,此时x=π/3
最终答案:略