Question 1031958: He all, Can somebody explain me the reason why for this equation:
tan(10° - 4x) = -1/3^(1/2)
the proposed solution is x=10°-k45° and not x=10°-k180°
This brings to the following 8 results in the first round of 360°:
10°, 55°, 100°, 145°, 190°, 235°, 280°, 325°
What causes this coeff k45° to be applied?
Thank you very much and regards
Answer by ikleyn(52866)   (Show Source):
You can put this solution on YOUR website! .
He all, Can somebody explain me the reason why for this equation:
tan(10° - 4x) = -1/sqrt(3)
the proposed solution is x=10°-k45° and not x=10°-k180°
This brings to the following 8 results in the first round of 360°:
10°, 55°, 100°, 145°, 190°, 235°, 280°, 325°
What causes this coeff k45° to be applied?
Thank you very much and regards
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tan(10° - 4x) =  --->
10° - 4x = -30° + k*180° (I wrote " + k*180° ", since 180° is the period of the tangent function).
From this equation we have
4x = 40° - k*180°, k = 0, +/-1, +/-2, . . .
and hence
x = 10° - k*45°, k = 0, +/-1, +/-2, . . .
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