How Do You Calculate Tensions in a Suspended Engine Setup?

[Ohoneo]

Finding tension -- really basic

Homework Statement

An automobile engine has a weight whose magnitude is 3150 N. The engine is positioned above an engine, and is positioned by a rope.
There is an illustration given, but it's essentially just saying that the angle concerning T1 is 10 degrees (and T1 is pointing up and slightly to the left), and the angle concerning T2 is 80 degrees and it is to the right and slightly down.
I'm supposed to find T1 and T2

Homework Equations

T = mg
W = mg
F = ma
x component = A cos theta
y component = A sin theta

The Attempt at a Solution

Here is what I did: I wrote out that Fx = - T1 cos 10 + T2 cos 80 = 0
Fy = T1 sin 10 - T2 sin 80 - W = 0
W = T1 sin 10 - T2 sin 80
T1 = (cos 80/cos 10) T2
Plug that into the equation solving for W.

W = (cos 80/cos 10) sin 10 - T2 sin 80
Solving for T2 I got approximately 3198 N.
Now, I stopped here, because the book said I was wrong.
Where I'm confused is that the book says that the x component for the tension involves sine and the y component involves cosine, but I was always taught it was the opposite... What am I missing here?

 

[gneill]

Where I'm confused is that the book says that the x component for the tension involves sine and the y component involves cosine, but I was always taught it was the opposite... What am I missing here?

If the angles are not in "the usual place", then it is quite possible for the sines and cosines to be interchanged. Perhaps you should post the diagram; your description of the angles and directions of the tensions leads me to believe that these aren't the "usual" angles.