Question

What quadrant(s) that all functions are negative in the unit circle? Is it even possible?

Answer 1

Having each function negative in the unit circle is not possible.

Explanation:

In the unit circle the quadrants have the following signs.
Quadrant I `(+,+)`
Quadrant II `(-,+)`
Quadrant III `(-,-)`
Quadrant IV `(+,-)`

Where #(x,y) are the coordinates of the graph.

For the trigonometric functions

Cosine - `cos = x`

Sine - `sin = y`
Secant - `sec = 1/x`
Cosecant - `csc = 1/y`
Tangent - `tan =y/x`
Cotangent - `ctn = x/y`

The six functions have the following signs in each quadrant: