且0<π/4<π/3<π/2,y=sin x在(0"," π/2)上是增加的,

　　∴sinπ/4

　　(2)∵△ABC为锐角三角形,

　　∴A∈(0"," π/2),且A+B>π/2,

　　∴A>π/2-B,且π/2-B∈(0"," π/2).

　　又y=sin x在(0"," π/2)上是增加的,

　　∴sin A>sin(π/2 "-" B),即sin A>cos B.

9.已知sin x+sin y=1/3,求M=sin x+sin2y-1的最大值与最小值.

解因为sin x+sin y=1/3,所以sin x=1/3-sin y.

　　因为-1≤sin x≤1,所以{■("-" 1≤1/3 "-" siny≤1"," @"-" 1≤siny≤1"," )┤

　　解得-2/3≤sin y≤1.

　　又易知M=sin x+sin2y-1=(siny"-" 1/2)^2-11/12,

　　所以当sin y=-2/3时,Mmax=4/9;

　　当sin y=1/2时,Mmin=-11/12.

B组　能力提升

1.函数y=|sin x|的一个单调递增区间是(　　)

A.("-" π/4 "," π/4) B.(π/4 "," 3π/4)

C.(π"," 3π/2) D.(3π/2 "," 2π)

解析画出函数y=|sin x|的图像(图略),易知选C.

答案C

2.导学号93774018定义在R上的奇函数f(x)的周期是π,当x∈[0"," π/2]时,f(x)=sin x,则f((2" " 021π)/3)的值为(　　)

A.-1/2 B.1/2 C.-√3/2 D.√3/2

解析f((2" " 021π)/3)=f((2" " 021π)/3 "-" 674π)=f("-" π/3)

　　=-f(π/3)=-sinπ/3=-√3/2.

答案C

3.已知α,β∈(0"," π/2),且cos α>sin β,则α+β与π/2的大小关系是(　　)

A.α+β>π/2 B.α+β<π/2

C.α+β≥π/2 D.α+β≤π/2

解析因为cos α>sin β,

　　所以sin(π/2 "-" α)>sin β.

　　而α,β∈(0"," π/2),

　　所以π/2-α∈(0"," π/2).

　　由y=sin x的单调性,知π/2-α>β,

　　所以α+β<π/2.

答案B

4.若函数y=sin x在[0,a]上是增加的,则a的取值范围为　　　　　　　　.