Question 212348This question is from textbook Advanced Mathematics
: Find all angles t such that 3t is coterminal with 180 degrees and t is between 0 degrees and 360 degrees.
This question is from textbook Advanced Mathematics
Found 2 solutions by HyperBrain, ikleyn:
Answer by HyperBrain(694)   (Show Source):
You can put this solution on YOUR website! I shall use modular arithmetic to solve this one.
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)
t=60 (mod 360)
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This is the general modular solution.
Algebraically,
t=360k+60
for all integer values of k
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
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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The solution in the post by @HyperBrain is wrong from the Math point of view.
It is also wrong from the teaching / pedagogical point of view.
I came to bring a correct solution and to teach you in a right way.
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'.
Solved correctly and completely and explained in a right way.
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