How do you find the exact value of $tan(pi/6)$ ?

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Answer 1 · 2016-04-08T10:22:31

$tan(pi/6)=1/sqrt(3)=sqrt(3)/3$

(see image below)
enter image source here
This is one of the standard trigonometric triangles.

$sqrt(3)$ has been determined using Pythagorean Theorem.

Sum of interior angles of a triangle is always $pi$ radians.

Answer 2 · 2016-04-08T10:24:08

$tan(pi/6) = sqrt3/3 approx 0.577$

Using the identity

$tan = sin/cos$ ,

and

$sin(pi/6) = sin(30) = 1/2$
$cos(pi/6) = cos(30) = sqrt3/2$

then

$tan(pi/6) = (1/2)/(sqrt3/2)$ .

You should know that dividing by one number is the same as multiplying by its reciprocal, so

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

Cancelling the $2$ 's and rationalising the denominator,

$1/2 * 2/sqrt3 = 1/sqrt3$
$1/sqrt3 * sqrt3/sqrt3 = sqrt3/3$

Therefore,

$tan(pi/6) = sqrt3/3$

Using a calculator,

$tan(pi/6) approx 0.577$

How do you find the exact value of tan(pi/6)tan(pi/6)?