tan x is negative so x could be in the 2nd or 4th quadrant. Cos x and sin x could be neg or positive.
3pi/2 < x < 2pi This is the 4th quad SO
Cos(x) is positive and sin(x) is negative
tanx = opp / add SO
opp=5 adj = 6 hypot = sqrt(25+36) = sqrt(61) [or a constant times these]
$$\\cos(x)=\frac{6}{\sqrt{61}}\\\\
sin(x)=-\frac{5}{\sqrt{61}}\\\\$$
tan x is negative so x could be in the 2nd or 4th quadrant. Cos x and sin x could be neg or positive.
3pi/2 < x < 2pi This is the 4th quad SO
Cos(x) is positive and sin(x) is negative
tanx = opp / add SO
opp=5 adj = 6 hypot = sqrt(25+36) = sqrt(61) [or a constant times these]
$$\\cos(x)=\frac{6}{\sqrt{61}}\\\\
sin(x)=-\frac{5}{\sqrt{61}}\\\\$$