Question

sin(-7派/12)=?cos(-61派/12)=?tan35派/12=?

已知属于sina=2/3,cos百塔=-3/4,a属于(派/2,派),百塔是第三象限角,求cos(a+百塔),sin(a-百塔)的值.

Answer 1

sin(-7派/12)=-sin(7派/12)=-(√6+√2)/4
cos(-61派/12)=cos(11派/12)=-cos(1派/12)=-(√6+√2)/4
tan35派/12=tan(-派/12)=-tan(派/12)=-(2-√3)=-2+√3

Answer 2

=-sin(7π/12)=-(√6+√2)/4
=-cos(π/12)=-(√6+√2)/4
=-tan(π/12)=√3-2

cosa=±√1-sin²a=±√5/3
a∈(π/2,π)
cosa=-√5/3
同理sinβ=-√7/4
cos(a+β)=√5/4+√7/6
sin(a-β)=-1/2-√35/12

Answer 3

sin(-7π/12)
=-cos(π/12)
=-((1+cosπ/6)/2)^0.5
=-((1+3^0.5/2)/2)^0.5

cos(-61π/12)
=-cos(π/12)
=-((1+3^0.5/2)/2)^0.5

tan(35π/12)
=tan(-π/12)
=((1-cos(-π/12))/(1+cos(-π/12)))^0.5