Solving Chandelier Problem: T1, Sine/Cosine Confusion

[cameuth]

1. A chandelier with mass is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension and makes an angle of with the ceiling. Cable 2 has tension and makes an angle of with the ceiling.




3. I have a free body diagram, but I'm not sure whether or not T1 in the y direction should have a sine or cosine in the Newton's second law equation. actually, I'm not sure how to determine sine or cosine for anything going in a direction not directly along the x or y-axis in a Newton's second law problem. Can anybody help?

 

[danago]

Whether you use sine or cosine depends on which angle you use (you could measure the angle that the string makes with the horizontal or with the vertical).

Draw a triangle with the tension in the cable to find its horizontal and vertical components. Label the angle that you know and then use trigonometry to determine whether you should use sine or cosine.

EDIT: Sorry, just saw that you specified the angle is with the ceiling. Still, draw a right angled triangle with the known angle and use trigonometry.

 

[cameuth]

so, for the x direction it would be:
T1cos(theta)-T2cos(theta)?

 

[danago]

Looks good to me; and that would be equal to zero, right?