Question 960664
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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.


<pre>
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

    {{{(5/13)^2}}} + {{{(12/13)^2}}} = {{{25/169}}} + {{{144/169}}} = {{{(25+144)/169}}} = {{{169/169}}} = 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".
</pre>

Solved.