Question

三角函数题1.Y=1-二分之一cos三分之π（派）X,X属于R2.Y=3sin(2X+四分之派）,X属于R3.Y=-二分

Answer 1

1、y=1-1/2cos(π/3x）当π/3x=2kπ,即x=6k k是整数,取最大值1+1/2=3/2

当π/3x=（2k+1）π,即x=6k+3 k整数,取最小值1-1/2=1/2

2、y=3sin(2x+π/4）当2x+π/4=2kπ+π/2,即x=kπ-π/8 k是整数,取最大值3

当2x+π/4=2kπ-π/2,即x=kπ-3π/8 k是整数,取最小值-3

3、y=-3/2cos(1/2x-π/6)当1/2x-π/6=2kπ,即x=4kπ+π/3 k是整数,取最小值-3/2

当1/2x-π/6=2kπ+π,即x=4kπ-7π/3 k是整数,取最大值3/2

4、y=1/2sin(1/2x+π/3）当1/2x+π/3=2kπ+π/2,即x=4kπ+π/3 k是整数,取最大值1/2

当1/2x+π/3=2kπ-π/2,即x=4kπ-5π/3 k是整数,取最小值-1/2