Answer:
sin theta = opp/hyp = √5/3 = (sq5)/3
csc theta = 1 / sin theta = 1 / (√5/3) = 1 x 3/√5 = 3/√5 = 3/(sq5)
csc theta = 3/(sq5) and tan theta = -(sq5)/2 = B
Step-by-step explanation:
if cos theta = -2/3
the -2 is adjacent
3 is the hypothenus
using pythagoras theorem
(hypothenus)² = (opposite)² + (adjacent)²
3² = opp²+ (-2)² = opp²+ (4)
9-4 = opp² = 5
opp = √5
sin theta = opp/hyp = √5/3 = (sq5)/3
tan theta = opp/adj = √5/-2 = (sq5)/2
csc theta = 1 / sin theta = 1 / (√5/3) = 1 x 3/√5 = 3/√5 = 3/(sq5)
csc theta = 3/(sq5) and tan theta = -(sq5)/2 = b
