Why is the arctan of equal to pi/6? My teacher says it's pi/6 but is it really that or is it pi/3? Maybe he messed up when providing the answer?

Question

arctan $sqrt3$

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Answer 1 · 2018-01-31T03:26:10

I think you are right, it is $pi/3$ that produces a tan of $sqrt3$

Tan is equal to $sin/cos$ , and for $pi/6$ , these values are

$sin(pi/3) = sqrt3/2$

$cos(pi/3)=1/2$

So, $tan(pi/3)=(sqrt3/2)/(1/2) = sqrt3$

So, $tan^(-1)sqrt3 = pi/3$