Verified answer

cos α = -√(3)/6 and α is in the third quadrant

Draw a triangle with the hypotenuse extending into the quadrant III.

Draw a vertical segment from the end of the hypotenuse to the x axis.

........................|

____-√3_______|______________

..|................./...|

..|√33......../.......|

..|........./..6........|

..|..../.................|

..|/.....................|

Using the pythagorean th, hypotenuse = 6,

Vert. segment has length √(33)

horizontal leg has length -√(3) where - denotes direction

sin α = o/h = √(33)/6

cos α = -√(3)/6

tan α = -√(33)√(3) = -√(11)