Question 1116152
.
<pre>
csc(3t) = 2    literally means


{{{1/sin(3t)}}} = 2    and is equivalent to


sin(3t) = {{{1/2}}}.


It has infinitely many solutions  in terms of 3t

3t = {{{pi/2 +- pi/3}}} + {{{2k*pi}}},  where  k is any integer  k = 0, +/-1, +/-2, . . . 


or, in terms of t


t = {{{pi/6 +- pi/9}}} + {{{2k*pi/3}}},  where  k is any integer  k = 0, +/-1, +/-2, . . . 


<U>Answer</U>.  The given equation has infinitely many solutions  t = {{{pi/6 +- pi/9}}} + {{{2k*pi/3}}},  where  k is any integer  k = 0, +/-1, +/-2, . . . 
</pre>