Pool ball hits table, find an angle

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The discussion revolves around the physics of a cue ball's collision with a pool table rail, specifically analyzing the angles and momentum involved. The initial conditions include a cue ball with a mass of 0.165 kg and an initial speed of 1.60 m/s at an angle of 30.0°. The key questions are determining the angle theta_2 after the bounce and calculating the change in linear momentum. The participant initially struggles with the trigonometric relationships and the coordinate system used in the problem but ultimately arrives at the correct answer for theta_2, which is 30 degrees. The confusion stems from understanding the notation and angle measurement conventions in the context of the problem.
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Figure 9-47 (attatched) shows a 0.165 kg cue ball as it bounces from the rail of a pool table. The ball's initial speed is 1.60 m/s, and the angle 1 = 30.0°. The bounce reverses the y component of the ball's velocity but does not alter the x component.

(a) What is theta_2?
(b) What is the change in the ball's linear momentum in unit-vector notation?

I got the physics of part b, the trig of part a is messing me up. I went so far as to make a system:
v\cos\theta_2=-v\cos\theta_1
v\sin\theta_2=v\sin\theta_1

As I thought! The angle must be in the second quadrant... so that means add 90 degrees, right? (And not 180-angle?)
But I don't know how to go from the typical coordinate system used for measuring angles to the funky one shown in the diagram.
 

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Never mind. I got the correct answer of 30 degrees (I had started out by saying theta_2 = -30 degrees). But why? How is that allowed? What kind of crazy notation are they using here (that apparently is standard...)?
 

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