Question

If sin x = -1/3 is in the 3rd quadrant and cos y = 2/5 is in the 4th quadrant, find the value of sec (x-y)

Answer 1

cos(x-y) = cosx cosy + sinx siny = (-√8/3)(2/5) + (-1/3)(-√21/5)

Answer 2

sin x = -1/3 is in the 3rd quadrant
then x = -1, r = 3 and
x^2 + y^2 = r^2
1 + y^2 = 9
y = √8 = -2√2
so we have cosx = -1/3, and sinx = -2√2/3

cos y = 2/5 is in the 4th quadrant
2^2 + y^2 = 25
y = -√21
so we have cosy = 2/5, and siny = -√21/5

cos(x-y) = cosxcosy + sinxsiny
= ... , you have those values, plug them in, then

sec(x-y) = 1/cos(x-y) , flip your fraction

Answer 3

Error!

In the first section , I interchanged sinx and cosx

go with ooblecks's numbers