Question 1203872
you are given that cot(theta) = 3
cot(theta) = adjacent side divided by opposite side.


if adjacent side is 3, then opposite side is 1.
use pythagorus to solve for hypotenuse.
pythagorus says that hypotenuse squared = adjacent side squared plus opposite side square.
you get hypotenuse squared = 3^2 + 1^2 = 9 + 1 = 10
this makes hypotenuse = sqrt(10)
you have:
adjacent side = 3
opposite side = 1
hypotenuse = 10


(a)
tan(𝛼) = opposite side / adjacent side = 1/3


(b)
csc(𝛼) = hypotenuse / opposite side = sqrt(10)/1 = sqrt(10)


(c)
sec(𝛼) = hypotenuse / adjacent side = sqrt(10)/3


(d)
sin(𝛼) = opposite side / hypotenuse = 1/sqrt(10)


here's a diagram with all the basic trig functions identified.


<img src = "http://theo.x10hosting.com/2023/092406.jpg">