[Physics] Simple derivation of the tension of a cord on a suspended mass

Question

Just wanted to disclaim this problem — it is homework. However, I am not asking for the solution, I am wondering if anyone can tell me what I may be doing wrong in solving this specific tension problem.

The problem is described by this picture:

Now, assuming masses of the cords suspending the mass $M$ are insignificant, the question is what is the value of $T_2$ (given specific values of $\theta$ and the mass of $M$).

So, here's my solution:

Since the object is in rest, by $F = ma$ and $a=g$,

$$ mg = T_1 \sin(\theta) $$

and

$$ T_2 = T_1 \cos(\theta) $$

Therefore,

$$ T_1 = \frac{mg}{\sin(\theta)} $$

and, furthermore,

$$ T_2 = \frac{mg \cos(\theta)}{\sin(\theta)} = mg \cot(\theta). $$

So, that is my final solution, however, multiple sources are telling me it is wrong (these sources being my 1. teacher's automated grading software and 2. a textbook answer to the same problem, with different mass and theta value and a value different than what I am finding).

Is this a correct means of reaching the conclusion?

Answer 1

Maybe I am missing something simple, but I cannot find any errors in your solution.