角α的终边上一点P(-3,4),求α的正弦余弦正切函数值.求使y=sinx-根号3下cosχ取得最大值和最小值的χ
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角α的终边上一点P(-3,4),求α的正弦余弦正切函数值.求使y=sinx-根号3下cosχ取得最大值和最小值的χ
角α的终边上一点P(-3,4),求α的正弦余弦正切函数值.求使y=sinx-根号3下cosχ取得最大值和最小值的χ
角α的终边上一点P(-3,4),求α的正弦余弦正切函数值.求使y=sinx-根号3下cosχ取得最大值和最小值的χ
(1)x=-3,y=4,r=5
sinα=y/r=4/5
cosα=x/r=-3/5
tanα=y/x=-4/3
(2)y=sinx-√3cosχ
=2[sinx*(1/2)-cosx*(√3/2)]
=2[sinxcos(π/3)-cosxsin(π/3)]
=2sin(x-π/3)
当 x-π/3=2kπ+π/2,即 x=2kπ+5π/6,k∈Z,y有最大值2
当 x-π/3=2kπ-π/2,即 x=2kπ-π/6,k∈Z,y有最小值-2
点P(-3,4)在第二象限
所以 sina>0 sina=4/根号下(3²+4²)=4/5
cosa<0 cosa=根号下(1-16/25)=-3/5
y=sinx-根号下3cosx
=2sin(x-π/3)
-2<=2sin(x-π/3)<=2
当2sin(x-π/3)=2
全部展开
点P(-3,4)在第二象限
所以 sina>0 sina=4/根号下(3²+4²)=4/5
cosa<0 cosa=根号下(1-16/25)=-3/5
y=sinx-根号下3cosx
=2sin(x-π/3)
-2<=2sin(x-π/3)<=2
当2sin(x-π/3)=2
sin(x-π/3)=1
x-π/3=2kπ+π/2
x=2kπ+5π/6
当2sin(x-π/3)=-2
sin(x-π/3)=-1
x-π/3=2kπ-π/2
x=2kπ-π/6
收起
|OP|=5
sina=4/5 cosa=-3/5 tana=-4/3
y=sinx-√3cosx=2sin(x-π/3)
所以最大值为2,此时x=5π/6+kπ
最小值为-2,此时x=-π/6+kπ