已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/16 00:36:17
已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值c

已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值
已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值

已知cosa=1/3,a∈(0,π)则cos(3/2π+2a)的值
cosa=1/3,a∈(0,π)
sina=2√2/3
cos(3/2π+2a)
=-sin(2a)
=-2sinacosa
=-4√2/9

sin(π/6-a)=cos[π/2-(π/6-a)]=cos(π/3+a)=1/3
cos(2π/3+2a)
=-cos[π-(2π/3+2a)]
=-cos(π/3-2a)
=-cos[2(π/6-a)]
=-[1-2sin²(π/6-a)]
=-[1-2×(1/3)²]
=-(1-2/9)
=-7/9