已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1(1)当x∈[0,π/2]时,求函数f(x)的最小值和最大值(2)设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3 f(C)=0 若向量m=(1,sinA)与向量n=(2,sinB)
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![已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1(1)当x∈[0,π/2]时,求函数f(x)的最小值和最大值(2)设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3 f(C)=0 若向量m=(1,sinA)与向量n=(2,sinB)](/uploads/image/z/1261364-68-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%E2%88%9A3sinxcosx-1%2F2cos%E2%88%A72x%2B1%2F2sin%E2%88%A72x-1%EF%BC%881%EF%BC%89%E5%BD%93x%E2%88%88%5B0%2C%CF%80%2F2%5D%E6%97%B6%2C%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%92%8C%E6%9C%80%E5%A4%A7%E5%80%BC%EF%BC%882%EF%BC%89%E8%AE%BE%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E4%B8%94c%3D%E2%88%9A3++f%EF%BC%88C%EF%BC%89%3D0+%E8%8B%A5%E5%90%91%E9%87%8Fm%3D%EF%BC%881%2CsinA%EF%BC%89%E4%B8%8E%E5%90%91%E9%87%8Fn%3D%EF%BC%882%2CsinB%EF%BC%89)
已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1(1)当x∈[0,π/2]时,求函数f(x)的最小值和最大值(2)设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3 f(C)=0 若向量m=(1,sinA)与向量n=(2,sinB)
已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1
(1)当x∈[0,π/2]时,求函数f(x)的最小值和最大值
(2)设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3 f(C)=0 若向量m=(1,sinA)与向量n=(2,sinB)共线 求a,b的值
谢谢
已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1(1)当x∈[0,π/2]时,求函数f(x)的最小值和最大值(2)设△ABC的内角A,B,C的对边分别为a,b,c,且c=√3 f(C)=0 若向量m=(1,sinA)与向量n=(2,sinB)
cos^2 x = (1+cos2x)/2
sin^2 x = (1-cos2x)/2
f(x) = sqrt(3)/2 sin2x - (1 + cos2x)/4 + (1 - cos2x)/4 - 1 = sqrt(3)/2 sin2x - 1/2 cos2x - 1
= sin(2x - pi/6) - 1
(1) 最大值0,最小sin(-pi/6) - 1 = -1.5
(2) f(C) = 0, 2C-pi/6 = pi/2, C = pi/3
sinA/1 = sinB/2
sinB = 2sinA
a/sinA = c/sinC = 2
a = 2sinA
b = 2sinB = 4sinA
b = 2a
a = 1, b = 2, c = sqrt(3)