Question

若a=sin(sin2009°),b=sin(cos2009°),c=cos(sin2009°),d=cos(cos2009°),则a,b,c,d从小到大的顺序是?

Answer 1

sin2009=sin151等于0.5
cos2009=cos151等于-sqr(3)/2
a=sin(0.5),b=-sin(sqr(3)/2),c=cos(0.5),d=cos(sqr(3)/2)
a>b,c>d
c>a
b和d,为负值,大小相反,d角度接近0,b角度接近1,所以d>b
a和d,d>a
所以C>D>A>B

Answer 2

sin2009=sin(600π+125)=sin55
cos2009=cos(600π+125)=-cos55
π/4>sin55>-cos55
sinsin55>sin(-cos55)
cos(-cos55)>cossin55
cossin55>sinsin55
coscos2009>cossin2009>sinsin2009>sincos2009

Answer 3

因2009°=360°*5+180°+29°所以sin2009°=sin（360°*5+180°+29°）=-sin29°，cos2009°=-cos29°，sin29°约为sin30°=0.5<cos29°约为cos30°=0.86所以a=-sin0.5，b=-sin0.86，c=cos0.5，d=cos0.86所以b<a<d<c

Answer 4

c>d>a>b
c=0.999964
d=0.99988
a=-0.00846
b=-0.01526