Question 958870: Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi]
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi]
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tan(x/8)+√3=0
tan(x/8)=-√3
x/8=2π/3, 5π/3
x=16π/3, 40π/3
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi)
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In his post, @lwsshar3 gives the answer x = 16π/3, 40π/3.
This answer is INCORRECT, since both these values are OUT of the interval [0,2pi).
See below my correct solution.
tan(x/8) + √3 = 0, (1)
tan(x/8) = -√3. (2)
We are looking for possible solutions 'x' in interval [ , ).
So, x/8 should be in interval [0, ), which is the same as interval [0, ).
But in this interval from 0 to , function tan is always non-negative.
Hence, equation (2) with the negative right side HAS NO solutions in this interval.
It implies that the original equation has no solution/solutions in the given interval [0,2pi). ANSWER
Solved correctly.
Ignore the post by @lwsshar3, since it is totally wrong.
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