SOLUTION: Please help understand the steps to answer this type of problem {{{ sqrt( 3 )tanx+1=0 }}}

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Question 1033267: Please help understand the steps to answer this type of problem
+sqrt%28+3+%29tanx%2B1=0+
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
What you wrote is possibly ambiguous: +sqrt%28+3+%29tanx%2B1=0+


sqrt%283%29%2Atan%28x%29%2B1=0, a best assumption.

sqrt%283%29tan%28x%29=-1

tan%28x%29=-1%2Fsqrt%283%29
You want to make some reference to an angle either in quadrant 2 or quadrant 4. You could ignore staying strictly to a unit-circle and just look at the sides of a right triangle. Imagine an angle pointing from origin into quadrant 4, because this will be easier to draw or visualize.

system%28y=1%2Cx=sqrt%283%29%2Cr=sqrt%281%5E2%2B%28sqrt%283%29%29%5E2%29%29

To continue with r, the hypotenuse for the triangle
r=sqrt%281%2B3%29
r=sqrt%284%29
r=2

This again would be for a angle x LESS THAN 0 measure, and going into quadrant 4.

Taking sin%28x%29, this is y%2Fr.
sin%28x%29=y%2Fr=1%2F2---------------------which will be 30 degrees, or pi%2F6.

Actually, for the original equation according to the assumption made, the actual answer can be EITHER 5pi%2F6 OR -pi%2F6.

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Please help understand the steps to answer this type of problem
+sqrt%28+3+%29tanx%2B1=0+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

sqrt%283%29%2Atan%28x%29+%2B+1 = 0,

sqrt%283%29%2Atan%28x%29 = -1,

tan%28x%29 = - 1%2Fsqrt%283%29  --->

x = 5pi%2F6  (Quadrant 2)  and/or  x = 11pi%2F6  (Quadrant 4)

in the interval [0,2pi).