SOLUTION: Please help me solve this equation: {{{tan x= - sqrt( 3 ) }}}.

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this equation: {{{tan x= - sqrt( 3 ) }}}.      Log On


   



Question 781743: Please help me solve this equation: tan+x=+-+sqrt%28+3+%29+.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
tan x= - sqrt( 3 )
-----
Draw a 30-60 degree right triangle.
Label the angles so you see where 30 degrees is
----
Let the side opposite the 30 degree angle be 1
Then the hypotenuse is 2
And the side opposite the 60 degree angle is sqrt(3)
----------
Notice that tan(60) = sqrt(3)/1 = sqrt(3)
--------
So 60 degrees is the reference angle.
--------
Then x = arctan(-sqrt(3)) is either 180-60 = 120 degrees
or x = arctan(-sqrt(3))is 360-60 = 300 degrees.
===============
Cheers,
Stan H.