How do you find the exact value of #tan(pi/3)#?

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Answer 1 · 2018-03-18T01:51:20

The value of #tan(pi/3)# is #sqrt3#.

We can use this fundamental trigonometric identity:

#tantheta=sintheta/costheta#

Here's a reference triangle with our #angletheta#:

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

Since we know #sin(pi/3)# is #sqrt3/2# and #cos(pi/3)# is #1/2#, we can use the previously stated identity to figure out the value of #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!