find the 5 other trig functions if cos(theta) = square root of 2/2 and cotangent is less than 0

Answer 1

if the cotØ < 0 then tanØ < 0
then Ø is in either II or IV
and since the cosØ = √2/2 (positive)
Ø is in I or IV
so Ø is in IV
the angle in standard position is 45°
(since cos45° = √2/2)

you should know the trig ratios of the 45° by heart.
so
sinØ = -√2/2
cscØ = -2/√2

cosØ = √2/2 --- the given value
secØ = 2/√2

tanØ = -1
cotØ = -1