find secθ if sinθ=(-4/5) and 270°<θ<360°?

Question

and explain, i worked it out a few times but got confused somewhere & know my answer is wrong much thanks if you can help =)

Answer 1

if sin x = -0.8
your calculator will give you
x = -53.13
To find the angle in the 4th quadrant, add 360 to it.
x = -53.13 + 360 = 306.87

Now find cos x = cos (306.87) = 0.6
sec x = 1/cosx = 5/3

Answer 2

now consider a right triangle
Take one of the angles other than 90 as θ
Now take 4 opp to θ and 5 on hypotenuse(without signs)
Generally the other side is 3
Now never mark hyp negative
Between 270°<θ<360° Sinθ is -ve so mark 4 -ve
Cosθ is +ve so mark 3 +ve
Now find secθ as 5/3

Answer 3

Will use Ø because I can`t find theta.
Can anyone help to find theta?!
Ø is in 4th quadrant and therefore cos Ø is positive.
cos Ø = 3 / 5
1/cos Ø = sec Ø = 5/3

Answer 4

sin8 = opposite side/hypotenuse= -4/5
adjacent side = sq.root of(hypotenuse squared- opposite side squared)
Adjacent side = sq.root of(25 - 16)
= sq.root of 9
= 3
cos 8= 3/5

therefore, sec 8 = 5/3