if csc=-13/5 what is the cot

Answer 1

cscx = -13/5 = 1/sinx

sinx =-5/13, cosx =either 12/13 or -12/13

cotx = cosx/sinx = either 12/5 or -12/5

cotx = 2.4 or -2.4

if pi<x<3pi/2 then cotx = 2.4

if 3pi/2 < x < 2pi then cotx = -2.4

Answer 2

3rd quadrant, where sine and cosine are both negative, so cotangent which is the ratio of cosine to sine, will be positive.

csc = 1/sin

since csc = -13/5,

then sin = -5/13

sin^2 + cos^2 = 1

so

(-5/13)^2 + cos^2 = 1

25/169 + cos^2 = 1

cos^2 = 144/169

cos = -12/13 (since in QIII)

cot = cos/sin = -12/13 / -5/13 = 12/5