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determine if it is possible for a number t to satisfy the given conditions sin(t) = 5/13 and cos(t) = 12/13.
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This problem assumes totally different solution from that in the post by @lwsshar3.
The only thing which you should to check is this equality
sin^2(t) + cos^2(t) = 1 (1)
for given values sin(t) and cos(t).
So, we calculate
+ = + = = = 1.
We see that equality (1) is held. It means that such an angle 't' (in radians) does exist
t = arcsin(5/13) = arccos(12/13).
Actually, 't' is the measure of an angle arctan(5/12).
So, the answer to the problem's question is "Yes".
Solved.