Find sec theta if sin theta = -4/5 and 270 degrees < theta < 360 degrees.

Answer 1

sin theta = -4/5 , so y=-4, r = 5

then r^2 = x^2 + y^2
25 = x^2 + 16
x = ±3 , but we are in quadrant IV, so x = +3
then cos theta = 3/5
and
sec theta = 5/3

Answer 2

We are talking a 3,4,5 right triangle here in the fourth quadrant.
Draw it
opposite down to the right 4 units
hypotenuse 5
adjacent from origin to x = +3
so
cos Theta = 3/5
sec T = 1/cos T = 5/3