问题标题:
已知cos(θ+π/2)=-1/2,求值已知cos(θ+π/2)=-1/2,求cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)的值
问题描述:
已知cos(θ+π/2)=-1/2,求值
已知cos(θ+π/2)=-1/2,求cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)的值
潘嘉林回答:
cos(θ+π)/sin(π/2-θ)[cos(3π-θ)-1]+cos(θ-2π)/cos(-θ)*cos(π-θ)+sin(θ+5π/2)
=
(-cosθ)/(cosθ)[-cosθ-1]+(cosθ/cosθ)*(-cosθ)+cosθ
=cosθ+1+(-cosθ)+cosθ
=cosθ+1
=√3/2+1或=-√3/2+1
cos(θ+π/2)=-1/2
sinθ=cos(π/2-θ)=1/2,cosθ=√3/2或cosθ=-√3/2
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