So we know that terminal side line is at quadrant III and that cosθ = -3/8
Triangle would look like what you see in attachment.
To find sinθ and tanθ, we need to find missing side length. We can use pythagorean theorem.
[tex]y^2 + (-3)^2 = (8)^2[/tex]
[tex]y= \sqrt{55}[/tex]
But since we are on quadrant III, y must be negative. Hence y = -√55
So sinθ = OPP / HYP = -√55 / 8
and tanθ = OPP / ADJ = - √55 / - 3 = √55 / 3
Hope this helps.
