已知sin(π+α)=根号3/2,求sin(3/4π-α)
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已知sin(π+α)=根号3/2,求sin(3/4π-α)
还有一题
急.在线等,给分
(1)由sin(π+α)=√3/2
∴sinα=-√3/2,
cosα=-1/2
∴sin(3π/4-α)
=sin3π/4cosα-cos3π/4sinα
=(√2/2)×(-1/2)-(-√2/2)(-√3/2)
=-√2/4-√6/4、.
(2)由[3sin(π+α)+cos(-α)]/[4sin(-α)-cos(9π-α)
(-3sinα+cosα)/(-4sinα+cosα)=2
∴-3sinα+cosα=-8sinα+2cosα
5sinα=cosα
∴tanα=sinα/cosα=1/5.
∴sinα=-√3/2,
cosα=-1/2
∴sin(3π/4-α)
=sin3π/4cosα-cos3π/4sinα
=(√2/2)×(-1/2)-(-√2/2)(-√3/2)
=-√2/4-√6/4、.
(2)由[3sin(π+α)+cos(-α)]/[4sin(-α)-cos(9π-α)
(-3sinα+cosα)/(-4sinα+cosα)=2
∴-3sinα+cosα=-8sinα+2cosα
5sinα=cosα
∴tanα=sinα/cosα=1/5.
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