Question

find the six trig functions is csc theta = 5 and cot theta <0

Answer 1

there is a picture of an angle whose cosecant is 5
the third side is found by pythagoras: it is \(\sqrt{5^2-1^2}=\sqrt{24}=2\sqrt{6}\)

Answer 2

you know that sine is positive, and cosine is negative, so you are in quadrant II
take the appropriate ratios to find all the other trig functions of the angle

Answer 3

ok can you please verify the answers for sec and tan

Answer 4

tangent is negative, and it is "opposite over adjacent" so it will be
\[-\frac{1}{2\sqrt{6}}\]