Question

how do I find the exact value of
tan^-1(-(1/sqrt3)) using the unit circle?

Answer 1

drawn above is a unit circle 30 deg angle with respect to x-axis...

Answer 2

we all know that tangent of an angle is the ratio between opposite side to adjacent side of the said angle....
\[\tan \theta = \frac{ o }{ a }\]

Answer 3

the angle that we are looking for is in the 2nd quadrant and 4th quadrant...

Answer 4

arctan( ) has a unique output in the interval.-pi/2 to pi/2

Answer 5

arctan[-1/sqrt(3)] exist at angles 5pi/6 (150 deg) and 11pi/6(330 deg)...

Answer 6

@orion1213 arctan( ) is a function and should only have one output per input (where that input is an element of the domain).

Answer 7

so there is 2 answers? how do I know which quadrant to look at?

Answer 8

thanks @myininaya, as a function, if the argument is negative, such that arctan (-x) = -arctan (x) so....
arctan [-1/sqrt(3)] = -arctan (1/sqrt(3)) = -30 degrees or -11pi/6...