Question 212348
.
This question is from textbook Advanced Mathematics
Find all angles t such that 3t is coterminal with 180 degrees and 0 <= t < 360 degrees.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution in the post by @HyperBrain is wrong from the Math point of view.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is also wrong from the teaching / pedagogical point of view.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring a correct solution and to teach you in a right way.



<pre>
An angle x is coterminal with 180 degrees if and only if when if is divided by 360, the remainder is 180.


So, 3t=180 (mod 360).


It means  3t = 180 + 360*k, k = 0, +/-1, +/-2, . . . (i.e., k is any integer).


In turn, it means that  t = 60 + 120*k.


Thus, t = 60 degrees (k=0),  or  t = 180 degrees (k=1)  or  t = 240 degrees (k=2).
    

We do not take other values of 'k', since it leads to outside of the given interval for 't'.
</pre>

Solved correctly and completely and explained in a right way.