作业帮高一必修4三角函数sin420*cos750+sin(-330)*cos(-660)tan675+tan765-tan(-330)+tan(-690)sin(25π/6)+cos(25π/3)+tan(-25π/4)2.已知sin(π+α)=-1/2 计算(1)sin(5π-α) (2)sin(π/2+α) (3)cos(α-3π/2) (4)tan(π/2-α)
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高一必修4三角函数sin420*cos750+sin(-330)*cos(-660)tan675+tan765-tan(-330)+tan(-690)sin(25π/6)+cos(25π/3)+tan(-25π/4)2.已知sin(π+α)=-1/2 计算(1)sin(5π-α) (2)sin(π/2+α) (3)cos(α-3π/2) (4)tan(π/2-α)
高一必修4三角函数
sin420*cos750+sin(-330)*cos(-660)
tan675+tan765-tan(-330)+tan(-690)
sin(25π/6)+cos(25π/3)+tan(-25π/4)
2.已知sin(π+α)=-1/2 计算
(1)sin(5π-α) (2)sin(π/2+α)
(3)cos(α-3π/2) (4)tan(π/2-α)
高一必修4三角函数sin420*cos750+sin(-330)*cos(-660)tan675+tan765-tan(-330)+tan(-690)sin(25π/6)+cos(25π/3)+tan(-25π/4)2.已知sin(π+α)=-1/2 计算(1)sin(5π-α) (2)sin(π/2+α) (3)cos(α-3π/2) (4)tan(π/2-α)
sin420*cos750+sin(-330)*cos(-660)
sin和cos周期是360,所以通过加或减360的整数倍
原式=sin60*cos30+sin30*cos60
=sin(60+30)
=sin90
=1
tan675+tan765-tan(-330)+tan(-690)
tan周期是180,所以也是加或减180的整数倍
原式=tan135+tan45-tan30+tan30
=-tan45+tan45-tan30+tan30
=0
sin(25π/6)+cos(25π/3)+tan(-25π/4)
=sin(25π/6-4π)+cos(25π/3-8π)+tan(-25π/4+6π)
=sin(π/6)+cos(π/3)+tan(-π/4)
=1/2+1/2-1
=0
2.已知sin(π+α)=-1/2 计算
(1)sin(5π-α)
sin(π+α)=-sinα=-1/2
sin(5π-α)=sin(π-α)=sinα=1/1
(2)sin(π/2+α)
sin²α+cos²α=1
所以cosα=±√3/2
sin(π/2+α)=cosα=±√3/2
(3)cos(α-3π/2)=cos(α-3π/2+2π)
=cos(α+π/2)
=-sinα
=-1/2
(4)tan(π/2-α)
=cotα
=1/tanα
=cosα/sinα
=±√3
sin420*cos750+sin(-330)*cos(-660)
=sin60cos30+sin30cos60
=sin(60+30)
=sin90
=1
tan675+tan765-tan(-330)+tan(-690)
=-tan45+tan45-tan30+tan30
=0
sin(25π/6)+cos(25π/3)+tan(...
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sin420*cos750+sin(-330)*cos(-660)
=sin60cos30+sin30cos60
=sin(60+30)
=sin90
=1
tan675+tan765-tan(-330)+tan(-690)
=-tan45+tan45-tan30+tan30
=0
sin(25π/6)+cos(25π/3)+tan(-25π/4)
=sin(π/6)+cos(π/3)+tan(-π/4)
=1/2+1/2-1
=0
2.已知sin(π+α)=-1/2 则-sina=-1/2 sina=1/2
cosa=（根号3）/2或者cosa=-（根号3）/2
(1)sin(5π-α)
=sina=1/2
(2)sin(π/2+α)
=cosa
=（根号3）/2或者-（根号3）/2
(3)cos(α-3π/2)
=cos(α+π/2)
=-sin α
=-1/2
(4)tan(π/2-α)
=cotα
=（根号3）
或者-（根号3）
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