Finding angle of change in momentum vector

[Patdon10]

Homework Statement

A billiard ball of mass m = 0.250 kg hits the cushion of a billiard table at an angle of θ1 = 55.8° at a speed of v1 = 27.2 m/s. It bounces off at an angle of θ2 = 71.0° and a speed of v2 = 10.0 m/s.

(a) What is the magnitude of the change in momentum of the billiard ball?
(I figured this out to be 5.667 kg*m/s)

(b) In which direction does the change of momentum vector point? (Let up be the +y positive direction and to the right be the +x positive direction.)
2Your answer is incorrect.° (counter-clockwise from the +x-axis)
(this is where I am absolutely stuck)

Homework Equations

tan^-1 (y component/x component)

The Attempt at a Solution

I calculated the velocities into x and y components and then found the change.
The change in the x component of the velocity is 13.81 m/s
The change in the y component of the velocity is -15.312 m/s
multiplying both by the mass of 0.25 kg, we get x = 3.4525, y = -3.828

so tan^-1(-3.828/3.4525) = -48 degrees, but that's not right. Can anyone tell me what I'm doing wrong?

 

[Patdon10]

anyone? : /