SOLUTION: Solve: tan (2theta - 34deg) = rad3 where theta is in the interval [real number of degrees]

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Question 874260: Solve: tan (2theta - 34deg) = rad3 where theta is in the interval [real number of degrees]
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
tan%282theta-34%5Eo%29=sqrt%283%29 has infinite solutions, unless the interval is restricted.
tan%2860%5Eo%29=sqrt%283%29 ,
so 2theta-34%5Eo=60%5Eo-->2theta=60%5Eo%2B34%5Eo-->2theta=94%5Eo-->theta=94%5Eo%2F2-->theta=47%5Eo is one answer.
However, tangent has a period of 180%5Eo , so many other answers are possible.
In general,
tan%2860%5Eo%2Bk%2A180%5E0%29=sqrt%283%29 for any k integer.
So all solutions can be found from
2theta-34%5Eo=60%5Eo%2Bk%2A180%5E0-->2theta=60%5Eo%2Bk%2A180%5E0%2B34%5Eo-->2theta=94%5Eo%2Bk%2A180%5E0-->theta=%2894%5Eo%2Bk%2A180%5E0%29%2F2-->theta=94%5Eo%2F2%2Bk%2A180%5E0%29%2F2-->theta=47%5Eo%2Bk%2A90%5E0
In the interval %22%5B+0+%2C%22360%5Eo%22%29%22 the solution is
for k=0 , theta=47%5Eo ,
for k=1 , theta=37%5Eo ,
for k=2 , theta=227%5Eo ,
for k=3 , theta=317%5Eo .