Key to "Find the value of tan⁡(π3)"

interdicoxd Answered2021-12-31

Find the value of

\tan (\frac{π}{3})

Answer & Explanation

Neil Dismukes

Expert

2022-01-01Added 37 answers

Well,

\tan (\frac{π}{3}) = \frac{\sin (\frac{π}{3})}{\cos (\frac{π}{3})} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \frac{\sqrt{3}}{2} (\frac{2}{1}) = \sqrt{3}

However, you can find it in another way:
Just think of it as a

\tan 60 °

and then draw a

30 ° - 60 ° - 90 °

tringle
And

\tan 60 °

will be equal to

\frac{o p p o s i t e}{a d j a c e n t}

in reference to

60 °

angle. Thus,

o p p o s i t e = \sqrt{3}

and

a d j a c e n t = 1

. Hence,

\tan 60 ° = \frac{o p p o s i t e}{a d j a c e n t} = \frac{\sqrt{3}}{1} = \sqrt{3}

twineg4

Expert

2022-01-02Added 33 answers

Use the Unit Circle and examine it at

\frac{π}{3}

And determine the tangent, if we know the point

({\frac{\sqrt{3}}{2}; {\frac{1}{2})

, thinking of it as a slope of the line in the unit circle.

\tan \frac{π}{3} = \frac{\frac{\sqrt{3}}{2} - 0}{\frac{1}{2} - 0} = \sqrt{3}

nick1337

Expert

2022-01-08Added 573 answers

$\tan (\frac{π}{3}) = \sqrt{3}$

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