1、sin(2π-α)=-sin α
cos(2π-α)=cos α
tan(2π-α)=-tan α
cot(2π-α)=-cot α
sec(2π-α)=sec α
csc(2π-α)=-csc α
2、图例解析如下：
1、∫sin(2π-α)dα
=-∫sin(2π-α)d(2π-α)
=cos(2π-α)+c
=cosα+c
2、图例解析如下：
1、
∫cos(2π-α)dα
=-∫cos(2π-α)d(2π-α)
=-sin(2π-α)+c
=sinα+c
2、图例解析如下：
1、∫tan(2π-α)dα
=-∫tan(2π-α)d(2π-α)
=-∫[sin(2π-α) d(2π-α)/ cos(2π-α)]
=∫d cos(2π-α)/cos(2π-α)
=ln|cos(2π-α)|+c
=ln|cosα|+c
2、图例解析如下：
1、∫cot(2π-α)dα
=-∫cot(2π-α)d(2π-α)
=-∫[cos(2π-α) d(2π-α)/ sin(2π-α)]
=-∫d sin(2π-α)/sin(2π-α)
=-ln|sin(2π-α)|+c
=-ln|sinα|+c
2、图例解析如下：
1、∫sec(2π-α)dα
=-∫d(2π-α)/ cos(2π-α)
=-∫cos(2π-α)d(2π-α)/ [cos(2π-α)]^2
=-∫dsin(2π-α)/ [1-(sin(2π-α))^2}
=-∫dsin(2π-α)/ [(1-sin(2π-α))(1+ sin(2π-α))]
=-(1/2)[∫dsin(2π-α)/ (1-sin(2π-α))+∫dsin(2π-α)/ (1+sin(2π-α))]
=-(1/2)ln{[1+sin(2π-α)]/ [1-sin(2π-α)]}+c
=-(1/2)ln[(1+sin(2π-α))/(1-sin(2π-α))]+c
=-(1/2)ln[(1+sin(2π-α))^2/(cos(2π-α))^2]+c
=-ln|(1+sin(2π-α))/cos(2π-α)|+c
=-ln|(1-sinα)/cosα|+c
=-ln|secα-tanα|+c
2、图例解析如下：
1、∫csc(2π-α)dα
=-∫csc(2π-α)d(2π-α)
=-∫d(2π-α)/ sin(2π-α)
=-∫sin(2π-α)d(2π-α)/ [sin(2π-α)]^2
=∫dcos(2π-α)/ [1-(cos(2π-α))^2]
=∫dcos(2π-α)/ [(1-cos(2π-α))(1+ cos(2π-α))]
=(1/2)[∫dcos(2π-α)/ (1-cos(2π-α))+∫dcos(2π-α)/ (1+cos(2π-α))]
=(1/2)ln[(1+cos(2π-α))/ (1-cos(2π-α))]+c
=(1/2)ln[(1+cos(2π-α))^2/(sin(2π-α))^2]+c
=ln|(1+cos(2π-α))/sin(2π-α)|+c
=ln|(1+cosα)/sinα|+c
=ln|cscα+cota|+c
2、图例解析如下：
