设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/15 00:53:50
设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值设函数f(

设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值
设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期
1.求f(π/2)的值
2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值

设函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期1.求f(π/2)的值2.已知f(a/2+π/12)=10/13,a∈(-π/2,0)求sin(a-π/4)的值
函数f(x)=2sin(wx+π/3)(w>0,x∈R),且以π为最小正周期
则T=2π/w=π
w=2
所以 f(x)=2sin(2x+π/3)
(1) f(π/2)=2sin(π+π/3)=-2sin(π/3)=-√3
(2)f(a/2+π/12)=2sin(a+π/6+π/3)=2cosa=10/13
cosa=5/13
a∈(-π/2,0)
sina=-12/13
sin(a-π/4)=sinacos(π/4)-cosasin(π/4)=-12/13*(√2/2)-(5/13)*(√2/2)=-17√2/26

(1) f(x)=2sin(wx-π/6)•sin(wx+π/2-π/6)
=2sin[π/2+(wx-π/6)]•sin(wx-π/6)
=2cos(wx-π/6)•sin(wx-π/6)
=sin(2wx-π/3)
因周期T=2π/2w=π,则w=1
所以f(x)=sin(2x-π/3)
在三角形ABC中,若A...

全部展开

(1) f(x)=2sin(wx-π/6)•sin(wx+π/2-π/6)
=2sin[π/2+(wx-π/6)]•sin(wx-π/6)
=2cos(wx-π/6)•sin(wx-π/6)
=sin(2wx-π/3)
因周期T=2π/2w=π,则w=1
所以f(x)=sin(2x-π/3)
在三角形ABC中,若A〈B,且f(A)=f(B)=1/2
则由f(x)=sin(2x-π/3)=1/2,
知2A-π/3=π/6,A=π/4
2x-π/3=π-π/6,B=7π/12
所以C=π-A-B=π-π/4-7π/12=π/6
由正弦定理BC/AB=sinA/sinC
=sin(π/4)/sin(π/6)
=(√2/2)/(1/2)
=√2
希望能帮到你,祝学习进步O(∩_∩)O

收起

设函数f(x)=sin(wx+t)(-π/2 设函数f(x)=sin(wx+t)(-π/2 设函数f(x)=sin(wx+φ)(w>0,-π/2 设函数f(x)=sin(wx+2π/3)+sin(wx-2π/3)(w>0)的最小正周期为π,求函数的单调区间? 设函数F(x)=sin(WX+fai)+cos(WX+fai) (W>0,fai的绝对值<π/2,) 的最小正周期为π,且F(-x)=F(x)则F(x)=? 设函数f(x)=sinwx+sin(wx-π/2),x属于R 若x=π/8是f(x)的一个零点,且0 设函数f(x)=sin(2wx+π/6)+1/2,(其中0 已知函数f(x)=sin wx-cos wx最小周期为π 求w 若f(a/2)=1/3求sin2a的值 函数y=cos^2wx-sin^2wx的最小正周期是π,则函数f(x)=2sin(wx+π/4)的一个单调递增函数y=cos^2wx-sin^2wx(w大于0)的最小正周期是兀,则函数y=2sin(wx+兀/4)的单调增区间是多少? 已知函数f(x)=sin(wx+π/6)+sin(wx-π/6)-2cos²wx/2,x∈R(其中w>0,)(1)求函数f(x)的值域 设函数f(x)=3sin(wx+π/6),w>0,x属于R,且以π/2为最小正周期(1)求f(0)?(2)求f(x)的解析式? 设函数f(x)=sin(wx-π/6)-2(cos∧2)(w/2)x+1(w>0),直线y=√3与函数y=f(x)图像...设函数f(x)=sin(wx-π/6)-2(cos∧2)(w/2)x+1(w>0),直线y=√3与函数y=f(x)图像相邻两交点的距离为π,求w的值 已知函数f(x)=sin(π/3+wx)+cos(wx-π/6)(w>0),f(x)多少最小正周期为π (1)求f(x)的解析式 (2)求f(x)单 设函数f(x)=3sin(wx+π/6),w>0 x∈(-∞,+∞),且以π/4为最小正周期 (设函数f(x)=3sin(wx+π/6),w>0 x∈(-∞,+∞),且以π/4为最小正周期 (1)求f(0) (2)求f(x)的解析式 (3)已知f(a/8+π/24 设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ| 设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ| 设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ| 设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|