已知cosx=1/3,-派/2

问题描述:

已知cosx=1/3,-派/2

数学人气:231 ℃时间:2019-10-11 21:47:08
优质解答
∵cosx=1/3,-π/2∴sinx=-√(1-cosx^2)=-√(1-1/9)=-2√2/3
∴tanx=sinx/cosx=(-2√2/3)/(1/3)=-2√2
∴sin(2π+x)/tan(-x-π)cos(-x)tanx
=-sinx/cosx(tanx)^2
=-(-2√2/3)/[(1/3)*(-2√2)^2]
=√2/4
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∵cosx=1/3,-π/2∴sinx=-√(1-cosx^2)=-√(1-1/9)=-2√2/3
∴tanx=sinx/cosx=(-2√2/3)/(1/3)=-2√2
∴sin(2π+x)/tan(-x-π)cos(-x)tanx
=-sinx/cosx(tanx)^2
=-(-2√2/3)/[(1/3)*(-2√2)^2]
=√2/4