Question

What are the cotangent, secant, and cosecant values on the Unit Circle?

Answer 1

You can find the value of `cot x` on the trig unit circle with origin `O`.
Suppose `M` is the extremity of the variable arc `AM = x`, and `B` is the top point of the circle. The line `AM` cut the horizontal tangent axis `Bz` at point `V`. The segment `BV` is the measure of `cot x`.
The trig unit circle only shows the 4 values of the 4 trig functions (`cos x`, `sin x`, `tan x`, `cot x`) of the arc `AM = x`. The unit circle doesn't show the values of `sec x` and `csc x`.

Answer 2

If `t` (or `theta`) is associated with the point `(x,y)` on the unit circle, then

`sint=y` `color(white)"sssssssssssssssssss"` `csct = 1/y` (for `y!=0`)

`cost=x` `color(white)"sssssssssssssssssss"` `sect = 1/x` (for `x!=0`)

`tant=y/x` (for `x!=0`)`color(white)"sssssss"` `cott = x/y` (for `y!=0`)