Question

已知角a的顶点在原点,始边在x轴的非负半轴重合,终边为射线3x+4y=0(x>=0),试求sina(sina+1/tan

Answer 1

3x+4y = 0,也就是 y = -3x/4,因此点(4,-3)在射线上.

这一点在第四象限,

sin(a) = y/r = y/sqrt(x^2+y^2) = -3/5,

cos(a) = x/r = 4/5,

tan(a) = y/x = -4/3,故

sina(sina+1/tana)+cos^2（a）

= (-3/5)(-3/5 - 3/4) + 16/25

= 29/20.

答案：29/20