Question

求大神解：已知sina=-8/17,且a第三象限,sin(a/2)=?,cos(a/2)=?？

Answer 1

a是第三象限角,
∴ 2kπ+π,8,sina = - 8/17
cosa = - √(17^2 - 8^2)/17 = - 15/17
a/2在第二象限
tan(a/2) = sina/(1 + cosa) = - 8/17/(1 - 15/17) = - 4
sin(a/2) = 4/√(1^2 + 4^2) = 4/√17
cos(a/2) = - 1/√(1^2 + 4^2) = - 1/√17,2,(sin(a/2)+cos(a/2))^2=1+sin(2a)=9/17
(sin(a/2)-cos(a/2))^2=1-sin(2a)=25/17
又由八卦图可得a/2为第二或第四象限角
分情况讨论解两个方程即得解,2,sin a = -8/17
按计算机得出 a = -28.072 = 331.9 OR a = 180 - 331.9 = -151.9 = 208.07
因为a是在third quadrant 所以应得出 a = 208.07
把a代进sin(a/2)和cos(a/2)便可得出答案,2,求大神解：已知sina=-8/17,且a第三象限,sin(a/2)=?,cos(a/2)=?
求详解