已知sin(a+π/6)=12/13,a+π/6属于第二象限,求cosa与sina的值
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![已知sin(a+π/6)=12/13,a+π/6属于第二象限,求cosa与sina的值](/uploads/image/z/2667197-29-7.jpg?t=%E5%B7%B2%E7%9F%A5sin%28a%2B%CF%80%2F6%29%3D12%2F13%2Ca%2B%CF%80%2F6%E5%B1%9E%E4%BA%8E%E7%AC%AC%E4%BA%8C%E8%B1%A1%E9%99%90%2C%E6%B1%82cosa%E4%B8%8Esina%E7%9A%84%E5%80%BC)
已知sin(a+π/6)=12/13,a+π/6属于第二象限,求cosa与sina的值
已知sin(a+π/6)=12/13,a+π/6属于第二象限,求cosa与sina的值
已知sin(a+π/6)=12/13,a+π/6属于第二象限,求cosa与sina的值
sin(a+π/6)=12/13
a+π/6∈(π/2,π)
cos(a+π/6)=-5/13
cosa
=cos(a+π/6-π/6)
=cos(a+π/6)cosπ/6+sin(a+π/6)sinπ/6
=-5/13*√3/2+12/13*1/2
=(12-5√3)/26
sina
=sin(a+π/6-π/6)
=sin(a+π/6)cosπ/6-cos(a+π/6)sinπ/6
=12/13*√3/2+5/13*1/2
=(12√3+5)/26