What Is the Solution for x in the Equation tan((πx)/2) = √(3)/2?

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The equation tan((πx)/2) = √(3)/2 can be approached by first recognizing that tan(x) = √(3)/2 leads to x = π/6 + πn due to the periodic nature of the tangent function. To solve for x in the original equation, one can set πx/2 = π/6 + πn and then solve for x. This results in x = (2/π)(π/6 + πn), simplifying to x = 1/3 + 2n. An important correction noted is that tan(π/6) equals 1/√3, not √(3)/2, suggesting that using arctan(√(3)/2) is preferable for clarity. The discussion emphasizes the need to solve for x while addressing the nuances of the tangent function's values.
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Homework Statement



tan((π(x))/2) = √(3)/2

Homework Equations


The Attempt at a Solution


tan(x) = √(3)/2
x= π/6 + πn, since Tan has a period of π
This is where I'm stuck
 
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tan(pi*x/2) = sqrt(3)/2
pi*x/2 = arctan(sqrt(3)/2)

x = (2*arctan(sqrt(3)/2))/pi

What is required of you? Find x?
 


Yea Find x
 


tonyviet said:
Yea Find x

Oh ok no problem
 
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I also found an x in your name! Funny that.

Well since for tan(x)=\frac{\sqrt{3}}{2}

x=\frac{\pi}{6}+\pi n

Then if we instead have tan\left(\frac{\pi x}{2}\right)=\frac{\sqrt{3}}{2}

We end up with \frac{\pi x}{2}=\frac{\pi}{6}+\pi n

and now solve for x. Simple, no? :smile:

EDIT: tan(\pi/6)=1/\sqrt{3}, not \sqrt{3}/2. Since it's not a nice number, it's best to leave it as arctan(\sqrt{3}/2)
 
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