solve the equation

Question

tan x + squareroot 3

solve for tan x

Answer 1

if tanx = sqr3 is the equation, then

x = the angle whose tangent is sqr3, with opposite side =sqr3 and adjacent side =1, hypotenuse = 2

x= pi/3, 4pi/3 or pi/3 +2npi or 4pi/3 + 2npi where n = any integer. There are an infinite number of solutions.

reference angle = pi/3 or 60 degrees

x = 60, 240, or 60+360n or 240+360n degrees where n = any integer

the angles are all in quadrant I or III

if the problem had restricted the solutions to 0<x<360 or 2pi

then there would have been 2 solutions: 60 and 240 degrees, or the equivalent in radians: pi/3 and 4pi/3

or sometimes the restriction in this type of problem is

that the solution is arctan(sqr3) where the range is -pi/2<x<pi/2

then there is only one solution, x=pi/3