The cosine of an obtuse angle is negative and the sine is positive.

Solution: rewrite the parameter equation of the straight line as {x =- 1-2/√ 5 * t, y =-1+1√ 5 * t,

The rectangular coordinate equation of the curve is (X- 1) 2+(Y- 1) 2 = 9.

(- 1-2/√5 * t- 1)2+(- 1+ 1/√5 * t- 1)2 = 9，

Simplified to t 2+4/√ 5 * t- 1 = 0,

Therefore t 1+t2 = -4/√5, t 1t2 =-1,

So the chord length = | t2-t1| = √ [(t1+t2) 2-4t1t2] = 6/√ 5.