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