Why is tan (pi/3) - sqrt (3) ? Without a calculator.

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Answer 1 · 2018-03-01T02:29:55

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$tan(pi/3) = sin(pi/3) / cos(pi/3)$

Using the unit circle/30 60 90 triangle properties,

$sin(pi/3) = sqrt(3)/2$
and
$cos(pi/3) = 1/2$

therefore $tan(pi/3) = (sqrt(3)/2)/ (1/2)$

Then simplify by multiplying the top and the bottom of the fraction by 2 to get:

$2/2 * (sqrt(3)/2)/ (1/2) = sqrt(3)/1 = sqrt3$

So,

$tan (pi/3) - sqrt (3)$

$sqrt (3) - sqrt (3)$

$0$