f(x)=a\sin b(x-c)の接線の傾きが実際にどうなるか調べましょう。

①スライダーを動かして、\
\ \ \ BをAに限りなく近づけましょう。

②やることその１\
Aを動かして、接線の傾きの軌跡が\
どうなるかを調べましょう。

②やることその２\
三角関数の係数を変えると、軌跡の形は\
変わるかを調べましょう。

a

クリーン

m

リセット

関数切り替え

A

B

f(x)=a\cos b(x-c)の接線の傾きが実際にどうなるか調べましょう

A

B

a

m

a

a

f(x)=a\tan b(x-c)の接線の傾きが実際にどうなるか調べましょう。

a

a

m

A

B

h_2 = 0 (slider from 0 to 10, step 0.1)
a_2 = 1 (slider from -5 to 5, step 0.1)
b_2 = 1 (slider from -5 to 5, step 0.1)
c_2 = 0 (slider from -5 to 5, step 0.1)
f_2(x) = (a_2 * tan((b_2 * (x - c_2))))
L = Point(f_2)
M: (x(L) + 2^((-h_2)), f_2(x(L) + 2^((-h_2))))
a = 1 (slider from -3 to 3, step 0.1)
b = 1 (slider from -3 to 3, step 0.1)
c = 0 (slider from -3 to 3, step 0.1)
h = 0 (slider from 0 to 10, step 0.1)
f(x) = (a * sin((b * (x - c))))
A = Point(f)
B: (x(A) + 2^((-h)), f(x(A) + 2^((-h))))
g = Line(A, B)
d: x(A)
e: x(B)
i: y(A)
j: y(B)
k: (j - i) / (e - d)
C: (x(A), k)
stage: 1
D: (x(A), 0)
l = Segment(A, D)
E: (0, k)
m = Segment(C, D)
n = Segment(C, E)
range = 33.3 (slider from -5 to 50, step 0.1)
min = 3 (slider from -5 to 5, step 0.1)
Red: (range * (min + a))
Green: (range * (min + b))
Blue: (range * (min + c))
flag1: true
flag2: false
function = 0 (slider from 0 to 2, step 1)
a_1 = 1 (slider from -5 to 5, step 0.1)
b_1 = 1 (slider from -5 to 5, step 0.1)
d_1 = 1 (slider from -5 to 5, step 0.1)
c_1 = 0 (slider from -5 to 5, step 0.1)
f_1(x) = (a_1 * cos((b_1 * (x - c_1))))
stage_1 = 1
h_1 = 0 (slider from 0 to 10, step 0.1)
F = Point(f_1)
G: (x(F) + 2^((-h_1)), f_1(x(F) + 2^((-h_1))))
p = Line(G, F)
o: x(F)
q: x(G)
r: y(F)
s: y(G)
t: (s - r) / (q - o)
H: (x(F), 0)
g_1 = Segment(F, H)
I: (x(F), t)
J: (x(I), 0)
K: (0, y(I))
i_1 = Segment(I, J)
j_1 = Segment(I, K)
flag1_1: true
flag2_1: true
range_1 = 33.3 (slider from -5 to 50, step 0.1)
min_1 = 5 (slider from -5 to 5, step 0.1)
Red_1: (range_1 * (min_1 + a_1))
Green_1: (range_1 * (min_1 + b_1))
Blue_1: (range_1 * (min_1 + c_1))
text13: "点Aの座標：(a,f(a))=" + (LaTeX[F]) + "\\
点Bの座標：" + (LaTeX[G]) + "\\
直線ABの傾き：m=\frac{" + (LaTeX[s]) + "-(" + (LaTeX[r]) + ")}{" + (LaTeX[q]) + "-(" + (LaTeX[o]) + ")}=" + (LaTeX[t]) + ""
text4: "点Aの座標：\ (a,f(a))=" + (LaTeX[A]) + "\\
点Bの座標：\ " + (LaTeX[B]) + "\\
直線ABの傾き：\ m=\frac{" + (LaTeX[j]) + "-(" + (LaTeX[i]) + ")}{" + (LaTeX[e]) + "-(" + (LaTeX[d]) + ")}=" + (LaTeX[k]) + ""
u: x(L)
v: x(M)
w: y(L)
stage_2 = 1
w_1: y(M)
k_2: (w_1 - w) / (v - u)
text19: "点Aの座標：(a,f(a))=(" + (LaTeX[u]) + "," + (LaTeX[w]) + ") \\
点Bの座標：(" + (LaTeX[v]) + "," + (LaTeX[w_1]) + ") \\
直線ABの傾き：m=\frac{ " + (LaTeX[w_1]) + "-( " + (LaTeX[w]) + ")}{" + (LaTeX[v]) + " -(" + (LaTeX[u]) + " )}=" + (LaTeX[k_2]) + " "
k_1 = Line(L, M)
N: (x(L), 0)
l_1 = Segment(L, N)
O: (x(L), k_2)
P: (x(O), 0)
Q: (0, k_2)
m_1 = Segment(O, P)
n_1 = Segment(O, Q)
flag1_2: true
flag2_2: true
Red_2: (range * (min_1 + a_2))
Green_2: (range * (min_1 + b_2))
Blue_2: (range * (min_1 + c_2))

Tool: Tool1
Input: A
Output: h, g

B: (x(A), 0)
C: (0, y(A))
g = Segment(A, C)
h = Segment(A, B)