How do you find the exact value of $tan (\frac{π}{3})$ $tan(pi/3)$ ?

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How do you find the exact value of $tan (\frac{π}{3})$ $tan(pi/3)$ ?

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Answer 1 · 2018-03-18T01:51:20

The value of $tan (\frac{π}{3})$ $tan(pi/3)$ is $\sqrt{3}$ $sqrt3$ .

Explanation:

We can use this fundamental trigonometric identity:

$tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$

Here's a reference triangle with our $∠ θ$ $angletheta$ :

![https://www.geogebra.org/geometry]( useruploads.socratic.org )

Since we know $sin (\frac{π}{3})$ $sin(pi/3)$ is $\frac{\sqrt{3}}{2}$ $sqrt3/2$ and $cos (\frac{π}{3})$ $cos(pi/3)$ is $\frac{1}{2}$ $1/2$ , we can use the previously stated identity to figure out the value of $tan (\frac{π}{3})$ $tan(pi/3)$ :

$tan(pi/3)=(quadsin(pi/3)quad)/cos(pi/3)$

$color(white)(tan(pi/3))=(quadsqrt3/2quad)/(1/2)$

$color(white)(tan(pi/3))=sqrt3/2*2/1$

$color(white)(tan(pi/3))=sqrt3/color(red)cancelcolor(black)2*color(red)cancelcolor(black)2/1$

$color(white)(tan(pi/3))=sqrt3/1*1/1$

$color(white)(tan(pi/3))=sqrt3/1*1$

$color(white)(tan(pi/3))=sqrt3/1$

$color(white)(tan(pi/3))=sqrt3$

That's the value of $tan(pi/3)$ . Hope this helped!

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How do you find the exact value of $tan (\frac{π}{3})$ $tan(pi/3)$ ?

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