The unit circle is an illustration of a circle with a radius equal to 1, with origin set in point (0,0). This circle can be used as a visible model to base all trigonometric functions, as the unit circle acts similarly to the periodic actions of these functions. For this reason, the unit circle is an important part of trigonometry.

Below is a graphical representation of the unit circle with quadrant I filled in with radian units and their coordinate points.

(0,1)
(1/2,sqrt(3)/2)
π/2
π/3
..od@@**X**@@eu..
.u@*"" X ^"#Rb.
u$"" X v "#N.
.d*" X e. "$u (sqrt(2)/2,sqrt(2)/2)
dP" X v "$u
u$" X e. "N. π/4
dP X v d$$c
8" X e. ..@P '#L
8" X v .dP #L
dF X e. ..@P $c (sqrt(3)/2,1/2)
J$ X v .dP '$ π/6
$\ X $. ..@P ...d$*k
4$ X v .dP ...d$$ '$
M> X. ..@P ...d$$ M>
$ X.pd ...d$$ ?k
$ XP...d$$ JR
(-1,0) 1π XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 0π / 2π (1,0)
$ X 4R
M> X M>
?k X $
'$ X J$
*k X $\
'$r X dP
'$ X xR
"$ X x$
^$. X JR
'$u X dP
"N. X u$"
'#N. X u$"
'"No. X .d*"
^"Rb.. X .u@*"
'""*@beo__X..ee@@*""
'""X"
(3π)/2
(0,-1)

The unit circle can be applied to any

trigonometric function, as shown below.

x = x coordinate
y = y coordinate
r = radius (1 in the unit circle)
sinθ = y/r cscθ = r/y
cosθ = x/r secθ = r/x
tanθ = y/x cotθ = x/y