已知a∈(0,π/2),sin(a+π/3)=3/5,则sina=?
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已知a∈(0,π/2),sin(a+π/3)=3/5,则sina=?
如果能顺便帮我总结一下以后碰到这种题型该怎么做就更好了
如果能顺便帮我总结一下以后碰到这种题型该怎么做就更好了
![已知a∈(0,π/2),sin(a+π/3)=3/5,则sina=?](/uploads/image/z/15338588-68-8.jpg?t=%E5%B7%B2%E7%9F%A5a%E2%88%88%280%2C%CF%80%2F2%29%2Csin%28a%2B%CF%80%2F3%29%3D3%2F5%2C%E5%88%99sina%3D%3F)
a∈(0,π/2),
a+π/3∈(π/3,5π/6),
cos(a+π/3)=-4/5
sina
=sin(a+π/3-π/3)
=sin(a+π/3)cosπ/3-cos(a+π/3)sinπ/3
=3/5*1/2+4/5*√3/2
=3/10+2√3/5
sin(a+π/3)=3/5
a+π/3∈(π/3,5π/6),
cos(a+π/3)=-4/5
sina
=sin(a+π/3-π/3)
=sin(a+π/3)cosπ/3-cos(a+π/3)sinπ/3
=3/5*1/2+4/5*√3/2
=3/10+2√3/5
sin(a+π/3)=3/5
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