You can put this solution on YOUR website! if the angle were in the first quadrant, then tan(x) would be positive and you would have tan(x) = sqrt(3)/3.
this equates to x = 30 degrees in the first quadrant.
you can use your calculator to solve for that or you can recognize that tan(x) = sqrt(3) / 3 is equivalent to tan(x) = 1/sqrt(3) which is part of a 30,60,90 degree triangle.
sin(30) = 1/2
cos(30) = sqrt(3)/2
tan(30) = sin(30)/cos(30) = 1/2 divided by sqrt(3)/2 which is equal to 1/sqrt(3) which is equivalent to sqrt(3)/3.
bottom line is that your angle is 30 degrees if it was in the first quadrant.
since the tangent is negative, then the angle can be in the second quadrant or in the fourth quadrant.
in the second quadrant, the angle would be 180 - 30 = 150 degrees.
in the fourth quadrant, the angle would be 360 - 30 - 330 degrees.
since each of these angles repeats every 360 degrees, then the angle will be:
150 degrees plus or minus 360 degrees.
330 degrees plus or minus 360 degrees.
a graph of y = tan(x) and the line of y = -sqrt(3)/3 is shown below:
the intersection of the line with the tangent function is where the solutions lie.
the solution is:
x = 150 plus or minus k * 360 degrees.
or
x = 330 plus or minus k * 360 degrees.
