
tan (3x) = 1
I know that 3x must be in quadrants II or IV
and I know that tan 45° = +1 or tan π/4 = 1
so 3x = π  π/4 OR 3x = 2π  π/4
3x = 3π/4 or 3x = 7π/4
x = π/4 or x = 7π/12
now the period of tan 3x is π/3
so adding multiples of π/3 to any answer will yield a new answer.
x = π/4
x = π/4 + π/3 = 7π/12 , we already have that one
x = 7π/12 + π/3 = 11π/12
x = 11π/12 + π/3 = 5π/4
x = 5π/4 + π/3 = 19π/12
x = 19π/12 + π/3 = 23π/12
The next one will be > 2π
So we have the above 6 solutions in the required domain.
btw, in degrees,
x = 45°, 105°, 165°, 225°, 285, and 345°
check two of them:
tan(3(105)) = 1
tan(3(345) = 1posted by Reiny
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