Unit Circle Trig Segments Reference
Author: Scott Farrar
Date: 29 November 2013

Drag Point A around the unit circle to observe
sin(Θ), cos(Θ), tan(Θ)
csc(Θ), sec(Θ), cot(Θ)

1

Sine

Cosine

Tangent

Cosecant

Secant

Cotangent

Unit Circle
Trigonometry

1

0

Compare Magnitudes

C = Intersect(xAxis, yAxis)
c = Circle(C, 1)
H, I = Intersect(c, xAxis)
h = Segment(H, I)
b = Segment(C, I)
A = Point(c)
g = OrthogonalLine(A, b)
Hypotenuse = Segment(C, A)
Θ = Angle(I, C, A)
B = Intersect(g, h)
Sine = Segment(A, B)
Cosine = Segment(C, B)
d, e = Tangent(A, c)
D = Intersect(d, yAxis)
E = Intersect(d, xAxis)
Cotangent = Segment(D, A)
Tangent = Segment(A, E)
radians = CircleArc(C, I, A)
Secant = Segment(C, E)
Radians: "radians = " + radians + " = " + (radians / 3.14159) + "π"
Degrees: "degrees = " + Θ
a = true
f = true
i = true
Cosecant = Segment(C, D)
j = true
k = true
l = true
T2: "Sin(Θ) = " + (sin(Θ))
T3: "Cos(Θ) = " + (cos(Θ))
T4: "Tan(Θ) = " + (tan(Θ))
T5: "Csc(Θ) = " + (1 / sin(Θ))
T6: "Sec(Θ) = " + (1 / cos(Θ))
F = (2, -0.1)
G = (1.5, -0.1)
poly1, m, n, p, q, J, K = Polygon(F, G, 4)
L = Point(n)
M = Point(n)
N = Point(n)
O = Point(n)
P = Point(n)
Q = Point(n)
T7_1: "cot(Θ) = " + (1 / tan(Θ)) + ""
o: abs((Sine * 0.5))
R = Point(Circle[L, abs((Sine * 0.5))])
r = Segment(L, R)
s_1: abs((Cosine * 0.5))
S = Point(Circle[M, abs((Cosine * 0.5))])
s = Segment(M, S)
t_1: abs((Tangent * 0.5))
T = Point(Circle[N, abs((Tangent * 0.5))])
t = Segment(N, T)
u: abs((Cosecant * 0.5))
U = Point(Circle[O, abs((Cosecant * 0.5))])
a_1 = Segment(O, U)
v: abs((Secant * 0.5))
V = Point(Circle[P, abs((Secant * 0.5))])
b_1 = Segment(P, V)
w: abs((Cotangent * 0.5))
W = Point(Circle[Q, abs((Cotangent * 0.5))])
c_1 = Segment(Q, W)