Question

若a=sin(sin2013°),b=sin(cos2013°),c=cos(sin2013°),d=cos(cos2013°),则a、b、c、d从小到大的顺序是

求详细过程，谢谢！

Answer 1

2013°=360°·3+213°

sin213°=-sin33°，cos213°=-cos33°.

∵cos33°>sin33°

∴-1<-cos33°<-sin33°<0.

y=sinx在(-π/2,0)上单调递增，所以sin(cos2013°)<sin(sin2013°)，即b<a

y=cosx在(-π/2,0)上单调递增，所以cos(cos2013°)<cos(sin2013°)，即d<c.

因为sin(sin2013°)=sin(-sin33°)=-sin(sin33°)<0，cos(cos2013°)=cos(-cos33°)=cos(cos33°)>0

所以b<a<d<c.

Answer 2

a=sin(sin2013°)=sin(sin213°)=sin(-sin33°)
b=sin(cos2013°)=sin(cos213°)=sin(-cos33°)
c=cos(sin2013°)=cos(sin213°)=cos(-sin33°)=cos(sin33°)
d=cos(cos2013°)=cos(cos213°)=cos(-cos33°)=cos(cos33°)
因sin33°<cos33°,所以0>-sin33°>-cos33°>-1
0>sin(-sin33°)>sin(-cos33°)>-1
因0<sin33°<cos33°<1
所以cos(sin33°)>cos(cos33°)>0
所以sin(-cos33°)<sin(-sin33°)<cos(cos33°)<cos(sin33°)
即b<a<d<c

Answer 3

b<a<c<d.画单位圆求解！这个东西只能自己体会，过程很难写的。不好意识啊！

追问

就是很难算才问的……尽量给出过程吧

追答

那我把过程写下来，拍成照片发给你好了！