It’s the special results which I compiled the other day

sin (2nd quadrant) = sin (basic)
cos (2nd quadrant) = - cos (basic)
Tan (2nd quadrant) = - Tan (basic)

sin (3rd quadrant) = - sin (basic)
cos (3rd quadrant) = - cos (basic)
Tan (3rd quadrant) = Tan (basic)

sin (4th quadrant) = - sin (basic)
cos (4th quadrant) = cos (basic)
Tan (4th quadrant) = - Tan (basic)

The ones which I mentioned same signage or opposite signages; these are the simplified results of the ASTC quadrants.

For the final point in the second page, they compiled the results for the fourth quadrant. If you realise, 360 - basic is the same position as -basic! This is because they are in the same position in the quadrant, separated by a full cycle of 360.

Sin (360 - basic) = - sin basic (since they have opposite signages in the first and the fourth quad)

cos (360 - basic) = cos basic (since they have the same signages in the first and the fourth quad)

Tan (360 - basic) = - Tan basic (since they have opposite signages in the first and the fourth quad)

Likewise, since -basic is is the same position as 360 - basic,

sin (-basic) = - sin (basic)
cos (-basic) = cos (basic)
Tan (-basic) = - Tan (basic)

for the 360-basic where did the 360 go tho
like sin(-x) = - sinx
the 360 is removed

the 1st 2nd 3rd quadrant thing is basically ASTC?

Remember that 360 - x and -x is the same position

The part where I mention the two angles are in the same position when you keep subtracting or adding 360

So of course Tan (360 - x) and tan (-x) is identical

Because their quadrant positions are identical

thx :)
btw can you help me with trigonometric functions and graphs + their properties etc?

The next section, which involves trigonometric functions and graphs, do not really make that much use of the quadrants diagram, but you must still know how they are related.

The section on trigonometric equation solving will require quadrants heavily.

what is trigonometric equation?
quadrants as in the 1st 2nd 3rd 4th quadrant right

That one is after graph sketching.

Trigo solving is like

Solve sin x = 1/2 for 0 to 360.

thx :)