Find secx if sinx = -4/5 and 270 < x < 360.

Question

tan^2x+1=sec^2x
(-4/5)^2+1=sec^2x
16/25+1=sec^2x
17/25=sec^2x
sqrt 17/5

I don't know if it should be positive or negative.

Answer 1

You are in the fourth quadrant
the secant has the same sign as the cosine, and in the fourth quadrant the cosine is positive,

Your answer is not correct

Here is an easier way than trying to use the formula you tried.
sinß = y/r = -4/5
so x^2 + (-4)^2 = 5^2
x = ±3 but you are in the fourth quadr, so x=+3
sec x = 1/cosx = 1/(3/5) = 5/3