若函数f(x)在[-π/2,π/2]上的最大值与最小值之和为根号3,求实数a的值.题目忘记打了- -已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).还有一题恩各种感谢TUT已知sin (α+π/3)+sinα=-4根
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![若函数f(x)在[-π/2,π/2]上的最大值与最小值之和为根号3,求实数a的值.题目忘记打了- -已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).还有一题恩各种感谢TUT已知sin (α+π/3)+sinα=-4根](/uploads/image/z/9312246-54-6.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%5B-%CF%80%2F2%2C%CF%80%2F2%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%8E%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B9%8B%E5%92%8C%E4%B8%BA%E6%A0%B9%E5%8F%B73%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC.%E9%A2%98%E7%9B%AE%E5%BF%98%E8%AE%B0%E6%89%93%E4%BA%86-+-%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28x%2B6%E5%88%86%E4%B9%8B%CF%80%29%2Bsin%28x-6%E5%88%86%E4%B9%8B%CF%80%29%2Bcosx%2Ba%28a%E5%B1%9E%E4%BA%8ER%2Ca%E6%98%AF%E5%B8%B8%E6%95%B0%29.%E8%BF%98%E6%9C%89%E4%B8%80%E9%A2%98%E6%81%A9%E5%90%84%E7%A7%8D%E6%84%9F%E8%B0%A2TUT%E5%B7%B2%E7%9F%A5sin+%28%CE%B1%2B%CF%80%2F3%29%2Bsin%CE%B1%3D-4%E6%A0%B9)
若函数f(x)在[-π/2,π/2]上的最大值与最小值之和为根号3,求实数a的值.题目忘记打了- -已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).还有一题恩各种感谢TUT已知sin (α+π/3)+sinα=-4根
若函数f(x)在[-π/2,π/2]上的最大值与最小值之和为根号3,求实数a的值.
题目忘记打了- -已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).
还有一题恩各种感谢TUT
已知sin (α+π/3)+sinα=-4根号3/5,-π/2
若函数f(x)在[-π/2,π/2]上的最大值与最小值之和为根号3,求实数a的值.题目忘记打了- -已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).还有一题恩各种感谢TUT已知sin (α+π/3)+sinα=-4根
f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a
=根号3/2sinx+1/2cosx+根号3/2sinx-1/2cosx+cosx+a
=根号3sinx+cosx+a
=2sin(x+π/6)+a
因为x∈[-π/2,π/2] 所以x+π/6 ∈[-π/3,2π/3]
由此可知f(x)最大值为2+a 此时x=π/3
f(x)最小值为-根号3+a 此时x=-π/2
于是得2+a+-根号3+a=2 解得a的值为二分之根号3
第二题-4根号3/5是负五分之4倍根号3 还是 -4倍的根号下(3/5) 把题说清楚
应该是负五分之4倍根号3 的话
sin (α+π/3)+sinα=-4根号3/5
即1/2sinα+根号3/2cosα+sinα=-4/5倍根号3
即3/2sinα+根号3/2cosα==-4/5倍根号3
两边同除以根号三得 根号3/2sinα+1/2cosα=-4/5 ①
即sin(x+π/3)=-4/5
又,-π/2<α<0 所以 x+π/3 ∈[-π/6,π/3] 即 cos(x+π/3)为正
则cos(x+π/3)=3/5
即1/2cosx-根号3/2sinx=3/5 ②
①+② 得cosx=-1/5
见图片