If cos theta = - 2/3 which of the following are possible?

A. sin theta = - (sq5) / 3 and tan theta = (sq5) / 2

B. csc theta = 3 / (sq5) and tan theta = - (sq5) / 2

C. csc theta = - 3/2 and tan theta = (sq5) / 2

D. sin theta = (sq5) / 3 and tan theta = (sq5) / 2

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