Find the exact value of cotθ given secθ=3 and tanθ<0.

Question

cotθ=8√/3
cotθ=−(3/√8)
cotθ=1/√8
cotθ=−(√8/3)
cotθ=−√8
cotθ=3/√8
cotθ=−(1/√8)
cotθ=√8

Is it cotθ=−(1/√8)?

thanks

Answer 1

cos =1/3 so positive x
cos/sin = negative so y is negative, quadrant 4
sin = - sqrt 8 / 3
cot = cos/sin= (1/3) / (- sqrt 8 /3) = -1 / sqrt 8
so yes

Answer 2

by the way sqrt 8 = 2 sqrt 2

Answer 3

correct