How do you find the six trig ratios?

For a general angle #theta#
#color(white)("XXXX")#Draw a right triangle such that #/_theta# is at the Cartesian origin and the right angle is on the X-axis.
#cos(theta) = "length of adjacent side" / "length of hypotenuse"#

#tan(theta) = "length of opposite side"/ "length of adjacent side"#

#csc(theta) = 1/sin(theta)#

#sec(theta) = 1/cos(theta)#

#cot(theta) = 1/tan(theta)#

The 4 main trig ratios are given by the trig unit circle.
AM = x is a variable arc, and M is the terminal point that rotates counterclockwise on the trig circle. The projection of the terminal M on 4 different axis of the trig unit circle defines the 4 trig functions: cos x, sin x, tan x and cot x
On the trig unit circle,
The segment Om = sin x . Om varies between - 1 and 1.
Segment On = cos x . On varies between -1 and 1.
Segment AT = tan x . AT varies from -infinity to +infinity
Segment BU = cot x. BU varies from -infinity to +infinity