Find tan B and csc B if sec B = 3/2 and tan B<0

Question

Use the Pythagorean identities to find each function value.

Answer 1

secx = 3/2 = hypotenuse/adjacent side

in quadrant IV

cosx = 2/3 = adjacent side/hypotenuse

sinx = opposite side/hypotenuse = -(sqr(9-4)/3 = -sqr5/3

cscx = 1/sinx = -3/sqr5

tanx = opposite side/adjacent side = sinx/cosx = -sqr5/2