How to find all 6 values

Question

sec(x)=-7/3, tan(x)<0

Answer 1

secx = -7/3, tanx <0 x is in quadrant II

secx = 1/cosx

cosx = -3/7

cosx = adjacent side over hypotenuse 1/secx = a/h =-3/7

secx = h/a = 7/(-3) h=7, a =-3

sinx = opposite side over hypotenuse = o/h = o/7

o^2 = h^2 -a^2 = 49-9 = 40

o = sqr40 = 2sqr10

sinx = (2/7)sqr10

cscx = 1/sinx = 7/2sqr10

tanx = o/a = (2sqr10)/(-3) = -(2sqr10)/3

cotx =a/o = 1/tanx = -3/2sqr10