f[x]=根号3乘sin2x+2cos方x+1,若tana=根号三/2,求f[a]
f[x]=根号3乘sin2x+2cos方x+1,若tana=根号三/2,求f[a]
f[x]=根号3乘sin2x+2cos方x+1,若tana=根号三/2,求f[a]
f[x]=根号3乘sin2x+2cos方x+1,若tana=根号三/2,求f[a]
f(x)
= √3 sin2x+2cos²x+1
=√3 sin2x+1+cos2x+1
=√3 sin2x+cos2x+2
tana=√3/2
然后用万能公式
sin2a=2tana/(1+tana^2)=2*√3/2/(1+3/4)=4√3/7
cos2a=(1-tana^2)/(1+tana^2)=(1-3/4)/(1+3/4)=1/7
所以f(a)=√3 sin2a+cos2a+2
=√3*4√3/7+1/7+2
=12/7+1/7+2
=27/7
7分之27 求采纳
函数f(x)=平方根3sin2x +2 COS ^ 2个+米简化获得
F(x)的=√3sin2x +1 + cos2x + M = 2sin(2X +π/ 6)+ M +1 函数f(x)的在区间[0,π/ 2],得到的最大值6 2 +米1米= 6,因此,= 3
(A)= 4 + 3根罪(2A +π/ 6)=√3/2
acosB + bcosA = C = csinC...
全部展开
函数f(x)=平方根3sin2x +2 COS ^ 2个+米简化获得
F(x)的=√3sin2x +1 + cos2x + M = 2sin(2X +π/ 6)+ M +1 函数f(x)的在区间[0,π/ 2],得到的最大值6 2 +米1米= 6,因此,= 3
(A)= 4 + 3根罪(2A +π/ 6)=√3/2
acosB + bcosA = C = csinC
所以C = 90度
所以2A +π/ 6 =π/ 3 A =π/12
塔纳= A / B =tanπ/12= 2 - √3
所以B = 2 /(2 - √3)= 4 +2√3
收起
f[x]=根号3乘sin2x+2cos方x+1
=根号3乘sin2x+cos2x
=2(根号3/2乘sin2x+1/2cos2x)
=2sin(2x+π/6)
tana=根号3/【3】
a=π/6
f(a)=2sin(2*π/6+π/6)
=2sinπ/2
=2