Question

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

Answer 1

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

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

Answer 2

A and B are correct!

Explanation:

Opposite side= - or +(sq5)

Adjacent side= -2

Hypotenuse= 3