I am having trouble with a task because I am having a hard time understanding when to use rad or deg.
The question is: "If $A$ is an obtuse angle in a triangle and $\sin A = \dfrac{5}{13}$, calculate the exact value of $\sin (2A)$."
How do I know if my calculator should be set to degrees or radians in this case?
Thanks in advance.
The short answer is that in the context of the specific question you cited, it is immaterial as to whether the angle $A$ is specified in degrees of radians.
From basic trigonometry, you can evaluate $\sin 2A$ directly in terms of $\sin A$ as
$$\sin 2A = 2\sin A\cos A = 2\sin A \sqrt{1-\sin^2 A}$$
The broader question as to whether an angle should be specified in radians or not depends, again, on the context.