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