- π /2

- π 

5 π /2

-2  π 

-5 π/2

-3 π 

-7 π/2

-4 π

4 π 

7 π /2

3 π 

-3 π /2

2 π

 π 

3 π /2

 π /2

0

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Ver

2

2

arco seno

arco coseno

arco tangente

secante

arco seno

arco coseno

arco tangente

secante

OX

OY

Origen

Oculta

Simetría

OX

OY

Origen

NO

Asíntotas hoizontales

Hor

Ocultar

Oblic

Hor

Ver

Oblic

Zoom

Aleja

Acerca

Derivadas

1ª

1ª

2ª

2ª

Crecimiento /

Decrecimiento

Concavidad /

Convexidad

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Ver

dada

T = 2 π 

T = π 

Impar:  sen(-x)=-sen(x)

Recta tangente

El arco como
función inversa

escala = 0.4 (slider from 0.2 to 1.4, step 0.2)
q = 1 (slider from 1 to 6, step 1)
f(x) = asin(x)
e1 = If(q ≟ 2, 0, -1.5707963267948966)
e2 = If(q ≟ 2, 3.141592653589793, 1.5707963267948966)
R2 = (1.5707963267948966, 0)
R1 = (-1.5707963267948966, 0)
u1 = Vector(R1, R2)
u2 = Vector((3.141592653589793, 0))
u3 = Vector((0, 0), (6.283185307179586, 0))
u = If(q ≟ 3, u1, Vector[If[q ≟ 6, u2, u3]])
t = 0.88 (slider from -0.1 to 1.3, step 0.001)
tt = Min(t, 1)
ttt = Max(0, tt)
dd = 1 (slider from 1 to 2, step 1)
a = 3 (slider from -5 to 5, step 1)
b = 0 (slider from 0 to 1, step 1)
c = 0 (slider from -5 to 5, step 1)
p = 3 (slider from -5 to 5, step 1)
texto2i: "(x+p)·(x-q) = (x-" + (LaTeX[p]) + ")·(x-" + (LaTeX[q]) + ")"
g_2(x) = f((-x))
P5: (0, f(0))
A, B, C, D, E_1, F, G, H, I, J, K, L, M = Roots(f, -20, 20)
ds = 0 (slider from 0 to 3, step 1)
g_1(x) = (-f(x))
f_1 = Mirror(f, y = 0)
f_2 = Mirror(f, x = 0)
dh = 0 (slider from 0 to 1, step 1)
dv = 0 (slider from 0 to 1, step 1)
do = 0 (slider from 0 to 1, step 1)
i = Limit(f, Infinity)
d1 = 0 (slider from 0 to 1, step 1)
d2 = 0 (slider from 0 to 1, step 1)
abscisa = -0.971 (slider from f1 to f2, step 0.001)
vv = 0 (slider from 0 to 1, step 1)
PX: (abscisa, 0)
k = OrthogonalLine(PX, xAxis)
P1 = Intersect(f, k, (-0.971, -1.329378594092521))
E1: P1
E2: P1
l = Segment(P1, PX)
E4: P1
E5: P1
dcr = 0 (slider from 0 to 1, step 1)
dco = 0 (slider from 0 to 1, step 1)
A2(x) = asin(x)
A3(x) = acos(x)
lista1 = Sequence((n * π), n, -10, 10)
lista2 = Sequence(x = Element[lista1, n], n, 1, 21)
lista3 = Sequence(x = Element[lista1 + π / 2, n], n, 1, 21)
listaa: {t01, t02, t03, t04, t05, t06, t07, t08, t10, t11, t12, t13, t14, t15, t16, t17, t18}
listab: {-12.57, -11, -9.42, -7.85, -6.28, -4.71, -3.14, -1.57, 0, 1.57, 3.14, 4.71, 6.28, 7.85398, 9.42478, 10.99557, 12.56637}
listac = Sequence((Element[listab, i], 0), i, 1, 17)
vp = 0 (slider from 0 to 1, step 0.1)
N = (-2.38, -9.08)
O = (-1, -8.82)
m = Segment(N, O)
uu: ((-ttt) * u)
h(x) = If[e1 ≤ x ≤ e2,f]
ht = Translate(h, uu)
texto5 = If(q ≟ 3 ∨ q ≟ 6, texto5b, texto5a)
P = (1.48, 1.58)
Q = (1.3, 3.42)
R = (-0.04, 3.44)
S = (-3.62, -2.04)
f_3 = Mirror(f, (0, 0))
listad = Sequence(Text[Element[listaa, k], Element[listac, k] - (0.1, 0.2)], k, 1, 17)
e = Tangent(P1, f)
A4(x) = atan(x)
B2(x) = sin(x)
B3(x) = cos(x)
B4(x) = tan(x)
fa(x) = sin(x)
df1 = Derivative(f, 1)
df2 = Derivative(f, 2)
listac1 = Sequence((0, Element[listab, i]), i, 1, 17)
listad1 = Sequence(Text[Element[listaa, k], Element[listac1, k] + (0.1, 0)], k, 1, 17)
P2 = Mirror(P1, d)
T = Intersect(d, l)
n = OrthogonalLine(T, yAxis)
f1 = If(q ≟ 3, ((-6.43364) * escala), -1)
f2 = If(q ≟ 3, (9.54818 * escala), 1)
ha(x) = If[e1 ≤ x ≤ e2,fa(x)]
r = OrthogonalLine(P1, yAxis)
PY = Intersect(r, yAxis)
V = Intersect(d, r)
s = OrthogonalLine(V, xAxis)
a_1 = OrthogonalLine(PY, r)
PX2 = Intersect(xAxis, s)
b_1 = Segment(PY, P1)
c_1 = Segment(PX2, P2)
d_1 = OrthogonalLine(P2, yAxis)
PY2 = Intersect(d_1, yAxis)
A_1 = Intersect(l, d_1)
B_1 = Intersect(ha, d_1, (1.526071237254345, 0.9989999998939556))
e_1 = Segment(PY2, P2)
p1: x(P1)
p2: y(P1)
q1: x(P2)
q2: y(P2)
A6 = NaN
texto6a: "arc sen ( " + p1 + " ) = " + p2 + ""
texto6b: "sen ( " + q1 + " ) = " + q2 + ""
texto6c: "arc cos ( " + p1 + " ) = " + p2 + ""
texto6d: "cos ( " + q1 + " ) = " + q2 + ""
texto6e: "arctan ( " + p1 + " ) = " + p2 + ""
texto6f: "tan ( " + q1 + " ) = " + q2 + ""
texto6 = If(q ≟ 1, texto6a, If[q ≟ 2, texto6c, texto6e])
texto66 = If(q ≟ 1, texto6b, If[q ≟ 2, texto6d, texto6f])
E = (-3.78, 1.96)
U = (0, 2)
ni = 0 (slider from 0 to 1, step 1)