Given an arc #AM = x# , with origin #A# and extremity #M#, that rotates on the trig unit circle with origin #O#.
The value of #cos x# is given by the projection of #M# on the horizontal #OAx#. #Om = cos x#.
The value of #sin x# is given by the projection of #M# on the vertical #OBy# axis. #On = sin x#. #B# is the top point of the trig circle.
Prolong the radius #OM# until it meets the vertical axis #AT# at #t#. the segment #At = tan x#.
Prolong the radius #OM# until it meets the horizontal #BZ# at #z#. The segment #Bz = cot x#.
In summary, the trig unit circle defines 4 trig functions of the arc #AM = x#. When the arc extremity #M# rotates, each function: #f(x) = cos x#; #f(x) = sin x#; #f(x) = tan x#; and #f(x) = cot x# varies along its own axis.
For example, the function #f(x) = sin x# varies from #1# to #-1# then back to #1# on the horizontal #OAx# axis.
For example, the function #f(x) = tan x# varies from #0# to #+infty# on the vertical #AT# axis, when #x# varies from #0# to #pi/2#. And #f(x) = tan x# varies from #-infty# to #0# when #x# moves from #pi/2# to #pi#.
