Interactive Unit Circle
Author: Cristine Fisher

\frac{\pi}{6}   \left( \frac{\sqrt{3}}{2},\frac{1}{2}   \right)

\frac{5\pi}{6}   \left(- \frac{\sqrt{3}}{2},\frac{1}{2} \right)

\frac{7\pi}{6}   \left(- \frac{\sqrt{3}}{2},-\frac{1}{2}\right) 

\frac{11\pi}{6}   \left( \frac{\sqrt{3}}{2},-\frac{1}{2}\right) 

Showπ/6

\frac{\pi}{4}   \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}   \right)

\frac{3\pi}{4}   \left(- \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}   \right)

\frac{5\pi}{4}   \left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}   \right)

\frac{7\pi}{4}   \left( \frac{\sqrt{2}}{2},- \frac{\sqrt{2}}{2}   \right)

Show π/4

\frac{\pi}{3}   \left(\frac{1}{2}, \frac{\sqrt{3}}{2}   \right)

\frac{2\pi}{3}   \left(-\frac{1}{2}, \frac{\sqrt{3}}{2}   \right)

\frac{4\pi}{3}   \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}   \right)

\frac{5\pi}{3}   \left(\frac{1}{2},- \frac{\sqrt{3}}{2}   \right)

Show π/3

0   (1,0)

\frac{\pi}{2}  (0,1)

π   (-1,0)

\frac{3\pi}{2}  (0,-1)

Show π/2

Unit Circle

\frac{2\pi}{6}   \left(\frac{1}{2}, \frac{\sqrt{3}}{2}   \right)

\frac{3\pi}{6}  (0,1)

\frac{4\pi}{6}   \left(-\frac{1}{2}, \frac{\sqrt{3}}{2}   \right)

\frac{6\pi}{6}   (-1,0)

\frac{8\pi}{6}   \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}   \right)

\frac{9\pi}{6}  (0,-1)

\frac{10\pi}{6}   \left(\frac{1}{2},- \frac{\sqrt{3}}{2}   \right)

Opp

Adj

Angle

Coordinates on the Circumference

e = 2.718281828459045
A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B = (0.8660254037844386, 0.5)
B' = Mirror(B, yAxis)
B'_1 = Mirror(B, xAxis)
B'' = Mirror(B', xAxis)
a = false
C = (0.7071067811865476, 0.7071067811865475)
C' = Mirror(C, yAxis)
C'' = Mirror(C', xAxis)
C''' = Mirror(C'', yAxis)
b = false
D = (0.5000000000000001, 0.8660254037844386)
D' = Mirror(D, yAxis)
D'' = Mirror(D', xAxis)
D''' = Mirror(D'', yAxis)
d = false
E = (1, 0)
F = (0, 1)
G = (-1, 0)
H = (0, -1)
f = false
I = Point(c)
g = Segment(I, A)
α = Angle(E, A, I)
J = (0.5, 0.866)
K = (0.003651471765389965, 1.0006783817843954)
L = (-0.5, 0.86603)
M = (-1, 0)
N = (-0.5, -0.86603)
O = (0, -1)
P = (0.5, -0.86603)
h = OrthogonalLine(I, xAxis)
Q = Intersect(h, xAxis)
i = Line(A, Q)
j = Segment(I, Q)
k = Segment(A, Q)
l = true
m = true
n = true
o = true