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20 votes
\tan\frac{5\pi}{7} x+\sqrt{3}=0

tan
7


x+
3

=0

1 Answer

5 votes

I'm guessing the equation is supposed to read


\tan\left(\frac{5\pi}7 x\right) + \sqrt3 = 0

Move the constant term to the other side:


\tan\left(\frac{5\pi}7 x\right) = -\sqrt3

Take the inverse tangent of both sides:


\tan^(-1)\left(\tan\left(\frac{5\pi}7 x\right)\right) = \tan^(-1)\left(-\sqrt3\right) + n\pi

(where n is an integer)


\frac{5\pi}7 x = - \tan^(-1)\left(\sqrt3\right) + n\pi

Since tan(π/3) = √3, we get


\frac{5\pi}7 x = -\frac\pi3 + n\pi

and solving for x gives


\boxed{x = -\frac7{15} + \frac{7n}5}

User Poisson
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