Question

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

Answer 1

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