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

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.