זהויות במעגל היחידה
Author: המרכז הארצי למורים למתמטיקה בחינוך העל יסודי

הקשר בין סינוס לקוסינוס

B

\Delta AOE\cong \Delta BOF

sinα = sin(180°-α)

\Delta AOE\cong \Delta COF

sinα = -sin(180°+α)

C

sinα = -sin(-α) = -sin(360°-α)

\Delta AOE\cong \Delta DOE

D

\Delta AOE\cong \Delta OGH

sinα = cos(90°-α)

G

sinα = -cos(90°+α)

\Delta AOE\cong \Delta OKL

K

\Delta AOE\cong \Delta OJL

sinα = -cos(270°-α)

J

sinα = cos(270°+α) 

\Delta AOE\cong \Delta OIH

I

זהויות של סינוס

cosα = -cos(180°-α)

cosα = -cos(180°+α)

cosα = cos(360°-α)=cos(-α)

זהויות של קוסינוס

A_1 = Intersect(xAxis, yAxis)
B_1 = Point(yAxis)
c = Circle(A_1, B_1)
C_1 = Intersect(c, xAxis, 2.0)
A = Point(c)
O = Intersect(xAxis, yAxis)
a = OrthogonalLine(A, xAxis)
E = Intersect(a, xAxis)
poly1, f, d, e = Polygon(A, O, E)
D = Intersect(c, a, 2.0)
b = Line(D, O)
B = Intersect(c, b, 2.0)
g = Line(O, A)
C = Intersect(c, g, 2.0)
poly2, o, f_1, d_1 = Polygon(E, D, O)
h = Line(B, C)
F = Intersect(h, xAxis)
poly3, h_1, e_1, o_1 = Polygon(B, O, F)
poly4, o_2, h_2, g_1 = Polygon(F, C, O)
α = Angle(E, O, A)
E' = Rotate(E, 90.0 * ° - α, O)
β = Angle(E, O, E')
i = Line(O, E')
G = Intersect(c, i, 2.0)
j = OrthogonalLine(G, xAxis)
H = Intersect(xAxis, j)
poly5, h_3, g_2, o_3 = Polygon(G, O, H)
I = Intersect(c, j, 2.0)
J = Intersect(c, i, 1.0)
k = OrthogonalLine(J, xAxis)
K = Intersect(c, k, 2.0)
poly6, o_4, h_4, i_1 = Polygon(H, I, O)
L = Intersect(k, xAxis)
poly7, l, o_5, k_1 = Polygon(O, K, L)
poly8, o_6, l_1, j_1 = Polygon(L, J, O)
m = false
γ = Angle(E, O, B)
n = false
δ = Angle(E, O, C)
p = false
ε = Angle(E, O, D)
q = false
poly9, f_2, o_7, b_1 = Polygon(O, B, F)
poly10, c_1, o_8, f_3 = Polygon(O, F, C)
poly11, d_2, e_2, o_9 = Polygon(E, O, D)
r = false
ζ = Angle(E, O, K)
s = false
η = Angle(E, O, J)
t = false
θ = Angle(E, O, I)
u = false
v = false
poly12, l_2, o_{10}, k_2 = Polygon(O, K, L)
poly13, j_2, o_{11}, l_3 = Polygon(O, L, J)
poly14, i_2, o_{12}, h_5 = Polygon(O, H, I)
w = false
poly15, h_6, o_{13}, g_3 = Polygon(O, G, H)
M = Point(yAxis)
N = Point(yAxis)
z = Vector(M, N)
P = Point(xAxis)
Q = Point(xAxis)
u_1 = Vector(P, Q)