三角関数の方程式の解を求めよう。

三角関数の方程式の解を求めよう。

ヒントの表示

正解

sc = Random(1, 2)
Mconst: {-1, -0.8660254037844386, -0.7071067811865476, -0.5, 0, 0.5, 0.7071067811865476, 0.8660254037844386, 1}
Mtextconst: {"-1", "-\frac{\sqrt{3}}{2}", "-\frac{\sqrt{2}}{2}", "-\frac{1}{2}", "0", "\frac{1}{2}", "\frac{\sqrt{2}}{2}", "\frac{\sqrt{3}}{2}", "1"}
M: {(0, 0), (0.5235987755982988, 0), (0.7853981633974483, 0), (1.0471975511965976, 0), (1.5707963267948966, 0), (2.0943951023931953, 0), (2.356194490192345, 0), (2.617993877991494, 0), (3.141592653589793, 0), (3.665191429188092, 0), (3.9269908169872414, 0), (4.1887902047863905, 0), (4.71238898038469, 0), (5.235987755982988, 0), (5.497787143782138, 0), (5.759586531581287, 0), (6.283185307179586, 0)}
A = Point(xAxis)
const = Random(1, 9)
textsc = If(sc ≟ 1, "\sin x", "\cos x")
textconst = Element(Mtextconst, const)
text1: "$0\leqq x<2\pi$の範囲で，$" + (LaTeX[textsc]) + "=" + (LaTeX[textconst]) + "$を満たす$x$の値の場所に
赤い点を正しく移動させよ．"
hint = 0
f = If(sc ≟ 1, sin(x), cos(x))
a: y = Element[Mconst, const]
sinSeikai1: {4.71238898038469, 4.1887902047863905, 3.9269908169872414, 3.665191429188092, 0, 0.5235987755982988, 0.7853981633974483, 1.0471975511965976, 1.5707963267948966}
sinSeikai2: {4.71238898038469, 5.235987755982988, 5.497787143782138, 5.759586531581287, 3.141592653589793, 2.617993877991494, 2.356194490192345, 2.0943951023931953, 1.5707963267948966}
B = Point(xAxis)
b: x(A) ≟ Element[sinSeikai1, const] ∧ x(B) ≟ Element[sinSeikai2, const]
c: x(A) ≟ Element[sinSeikai2, const] ∧ x(B) ≟ Element[sinSeikai1, const]
cosSeikai1: {3.141592653589793, 2.617993877991494, 2.356194490192345, 2.0943951023931953, 1.5707963267948966, 1.0471975511965976, 0.7853981633974483, 0.5235987755982988, 0}
cosSeikai2: {3.141592653589793, 3.665191429188092, 3.9269908169872414, 4.1887902047863905, 4.71238898038469, 5.235987755982988, 5.497787143782138, 5.759586531581287, 0}
d: x(A) ≟ Element[cosSeikai1, const] ∧ x(B) ≟ Element[cosSeikai2, const]
e: x(A) ≟ Element[cosSeikai2, const] ∧ x(B) ≟ Element[cosSeikai1, const]
bc: (b ∨ c) ∧ (const ≠ 1) ∧ (const ≠ 9)
de: (d ∨ e) ∧ (const ≠ 1) ∧ (const ≠ 9)
bc2: (x(A) ≟ Element[sinSeikai1, const] ∨ x(A) ≟ Element[sinSeikai2, const]) ∧ (const ≟ 1 ∨ const ≟ 9)
de2: (x(A) ≟ Element[cosSeikai1, const] ∨ x(A) ≟ Element[cosSeikai2, const]) ∧ (const ≟ 1 ∨ const ≟ 9)
answer: bc ∨ bc2 ∨ de ∨ de2