If cos t 513 and if the terminal point determined by t is i

If cos t = 5/13 and if the terminal point determined by t is in Quadrant III, find

tan t cot t + csc t.

Solution

cos t=-5/13

sin t=opposite/hypotenuse= -12/13

tant=sint/cost= 12/5

cot t=1/tan t=5/12 and csct=1/sint=-13/12

therefore tan t cot t + csct= (12/5)(5/12) +(-13/12)= 1-13/12=-1/12