§8　函数y=Asin(ωx+φ)的图像与性质

A组　基础巩固

1.函数y=2sin(2x+π/6)+1的最大值是(　　)

A.1 B.2 C.3 D.4

解析函数y=2sin(2x+π/6)+1的最大值为2+1=3.

答案C

2.已知函数f(x)=sin(ωx+π/3)(ω>0)的最小正周期为π,则f(π/6)=(　　)

A.-√3/2 B.√3/2 C.1/2 D.-1/2

解析由2π/ω=π,得ω=2,此时f(x)=sin(2x+π/3).

　　∴f(π/6)=sin(π/3+π/3)=√3/2.

答案B

3.函数y=3sin(π/4 "-" x)的一个单调递减区间为(　　)

A.["-" π/2 "," π/2] B.["-" π/4 "," 3π/4]

C.[3π/4 "," 7π/4] D.["-" 3π/4 "," π/4]

解析y=3sin(π/4 "-" x)=-3sin(x"-" π/4),当x∈["-" π/4 "," 3π/4]时,x-π/4∈["-" π/2 "," π/2],此时y=sin(x"-" π/4)在区间["-" π/4 "," 3π/4]上是增加的,从而y=-3sin(x"-" π/4)在区间["-" π/4 "," 3π/4]上是减少的,即单调递减区间是["-" π/4 "," 3π/4].

答案B

4.在同一平面直角坐标系中,函数y=cosx/2+3π/2(x∈[0,2π])的图像和直线y=1/2的交点个数是(　　)

A.0 B.1 C.2 D.4

解析作出函数y=cosx/2+3/2π,x∈[0,2π]的图像及y=1/2的图像可得,应选C.

答案C

5.

已知函数y=sin(ωx+φ)(ω>0",|" φ"|" <π/2)的部分图像如图所示,则(　　)

A.ω=1,φ=π/6

B.ω=1,φ=-π/6

C.ω=2,φ=π/6

D.ω=2,φ=-π/6

解析∵T=4×(7π/12 "-" π/3)=π,

　　∴ω=2π/T=2,由五点作图法知2×π/3+φ=π/2,φ=-π/6.

答案D

6.