已知cos(75°+θ)=1/3,θ为第三象限角,求cos(-225°-θ)+sin(435°+θ)的值.
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已知cos(75°+θ)=1/3,θ为第三象限角,求cos(-225°-θ)+sin(435°+θ)的值.
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/>cos(75°+θ)=1/3,θ为第三象限角
设 75°+θ=A
∴ θ=A-75°
则 cosA=1/3, A是第四象限角
∴ sinA=-√(1-cos²A)=-2√2/3
cos(-225°-θ)+sin(435°+θ)
=cos(225°+θ)+sin(435°+θ)
=cos(225°+A-75°)+sin(435°+A-75°)
=cos(150°+A)+sin(360°+A)
=cos150°cosA-sin150°sinA+sinA
=(-√3/2)*(1/3)-(1/2)*(-2√2/3)+(-2√2/3)
=-√3/6 -2√2/3
设 75°+θ=A
∴ θ=A-75°
则 cosA=1/3, A是第四象限角
∴ sinA=-√(1-cos²A)=-2√2/3
cos(-225°-θ)+sin(435°+θ)
=cos(225°+θ)+sin(435°+θ)
=cos(225°+A-75°)+sin(435°+A-75°)
=cos(150°+A)+sin(360°+A)
=cos150°cosA-sin150°sinA+sinA
=(-√3/2)*(1/3)-(1/2)*(-2√2/3)+(-2√2/3)
=-√3/6 -2√2/3
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