please help me!!evaluate the expressions: arctan(-√3)Arctan(-√3)

Solution:- To evaluate [tex]tan^{-1}(-\sqrt{3} )[/tex]Consider a right angle triangle with base angle x =[tex]tan^{-1}(-\sqrt{3} )[/tex]⇒tan x = [tex](-\sqrt{3} )[/tex] We know that for[tex]\theta[/tex]=60°,  tan(60°)=[tex]\sqrt{3}[/tex]here the value is [tex](-\sqrt{3} )[/tex] so it will lie in 2nd or 4th quadrant.For 2nd quadrant the value of x will be x=180°-[tex]\theta[/tex]⇒ x=180°-60°=120°.For 4th quadrant the value of x will be x=360°-[tex]\theta[/tex]⇒ x=360°-60°=300°.In radian For 2nd quadrant the value of x will be x=180°-[tex]\theta[/tex]⇒[tex]x=\pi-\frac{\pi}{3}=\frac{2\pi}{3}[/tex] =1.04(approx)For 4th quadrant the value of x will be x=360°-[tex]\theta[/tex]⇒[tex]x=2\pi-\frac{\pi}{3}=\frac{5\pi}{3}[/tex] .