2D 座標架
Author: 藍邦偉  老師

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廣義角的特別角(4)

O = Intersect(x = 0, y = 0)
Q_2: 0.65 * Corner[1] + 0.35 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
n = 0 (slider from 0 to 23, step 1)
α = Angle((1, 0), O, (cos((n * 15)°), sin((n * 15)°)))
r = Ray(O, (cos((n * 15)°), sin((n * 15)°)))
r_0 = Ray(O, (1, 0))
s_0 = Segment((0.5 * cos((n * 15)°), 0.5 * sin((n * 15)°)), (2.5 * cos((n * 15)°), 2.5 * sin((n * 15)°)))
P = Point(s_0)
tri, c, b, a = Polygon(P, O, (x(P), 0))
B = Mirror(P, yAxis)
C = Mirror(P, O)
D = Mirror(P, xAxis)
tri_a, c_1, a_1, b_1 = Polygon(O, B, (x(B), 0))
tri_b, c_2, a_2, b_2 = Polygon(O, C, (x(C), 0))
tri_c, c_3, a_3, b_3 = Polygon(O, D, (x(D), 0))
B_1 = Intersect(r, x = x(Corner[2]))
B_2 = Intersect(r, y = y(Corner[3]))
B_3 = Intersect(r, x = x(Q_2))
B_4 = Intersect(r, y = y(Corner[2]))
u_1 = Vector(O, B_1)
u_2 = Vector(O, B_2)
u_3 = Vector(O, B_3)
u_4 = Vector(O, B_4)
A = (-5.84781289240647, 1.9745757667038337)
text00: "$sin0°≈\frac{\fgcolor{669900}0}{\fgcolor{blue}" + (LaTeX[c]) + "}=0$
$\;$
$cos0°≈\frac{\fgcolor{red}{{" + (LaTeX[c]) + "}}}{\fgcolor{blue}" + (LaTeX[c]) + "}=1$
$\;$
$tan0°≈\frac{\fgcolor{669900}0}{\fgcolor{red}{" + (LaTeX[c]) + "}}=0$"
text01: "$sin15°≈\frac{\fgcolor{669900}{" + (LaTeX[y(P)]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6-\sqrt2}{4}$
$cos15°≈\frac{\fgcolor{red}{" + (LaTeX[x(P)]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6+\sqrt2}{4}$
$tan15°≈\frac{\fgcolor{669900}{" + (LaTeX[y(P)]) + "}}{\fgcolor{red}{" + (LaTeX[x(P)]) + "}}=2-\sqrt3$"
text02: "$sin30°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{2}$
$cos30°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt3}{2}$
$tan30°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=\frac{1}{\sqrt3}$"
text03: "$sin45°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{\sqrt2}$
$cos45°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{\sqrt2}$
$tan45°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=1$"
text04: "$sin60°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt3}{2}$
$cos60°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{2}$
$tan60°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=\sqrt3$"
text05: "$sin75°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6+\sqrt2}{4}$
$cos75°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6-\sqrt2}{4}$
$tan75°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=2+\sqrt3$"
text06: "$sin90°≈\frac{\fgcolor{669900}{" + (LaTeX[c]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=1$
$\;$
$cos90°≈\frac{\fgcolor{red}0}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=0$
$\;$
$tan90°≈\frac{\fgcolor{669900}" + (LaTeX[c]) + "}{\fgcolor{red}0}⇒無意義$"
text07: "$sin105°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6+\sqrt2}{4}$
$cos105°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6-\sqrt2}{4}$
$tan105°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=-(2+\sqrt3)$"
text09: "$sin135°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{\sqrt2}$
$cos135°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{\sqrt2}$
$tan135°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=-1$"
text10: "$sin150°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{2}$
$cos150°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt3}{2}$
$tan150°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=-\frac{1}{\sqrt3}$"
text11: "$sin165°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6-\sqrt2}{4}$
$cos165°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6+\sqrt2}{4}$
$tan165°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=-(2-\sqrt3)$"
text12: "$sin180°≈\frac{\fgcolor{669900}0}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=0$
$\;$
$cos180°≈\frac{\fgcolor{red}{-" + (LaTeX[c]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-1$
$\;$
$tan180°≈\frac{\fgcolor{669900}0}{\fgcolor{red}{-" + (LaTeX[c]) + "}}=0$"
text13: "$sin195°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}" + (LaTeX[c]) + "}}=-\frac{\sqrt6-\sqrt2}{4}$
$cos195°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6+\sqrt2}{4}$
$tan195°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=2-\sqrt3$"
text14: "$sin210°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{2}$
$cos210°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt3}{2}$
$tan210°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=\frac{1}{\sqrt3}$"
text15: "$sin225°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{\sqrt2}$
$cos225°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{\sqrt2}$
$tan225°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=1$"
text16: "$sin240°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt3}{2}$
$cos240°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{2}$
$tan240°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=\sqrt3$"
text17: "$sin255°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6+\sqrt2}{4}$
$cos255°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6-\sqrt2}{4}$
$tan255°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=2+\sqrt3$"
text18: "$sin270°≈\frac{\fgcolor{669900}{-" + (LaTeX[c]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-1$
$\;$
$cos270°≈\frac{\fgcolor{red}{0}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=0$
$\;$
$tan270°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}0}⇒無意義$"
text19: "$sin285°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6+\sqrt2}{4}$
$cos285°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6-\sqrt2}{4}$
$tan285°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=-(2+\sqrt3)$"
text20: "$sin300°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt3}{2}$
$cos300°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{2}$
$tan300°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=-\sqrt3$"
text21: "$sin315°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{\sqrt2}$
$cos315°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{1}{2}$
$tan315°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=-1$"
text22: "$sin330°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{2}$
$cos330°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt3}{2}$
$tan330°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=-\frac{1}{\sqrt3}$"
text23: "$sin345°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{\sqrt6-\sqrt2}{4}$
$cos345°≈\frac{\fgcolor{red}{" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt6+\sqrt2}{4}$
$tan345°≈\frac{\fgcolor{669900}{-" + (LaTeX[a]) + "}}{\fgcolor{red}{" + (LaTeX[b]) + "}}=-(2-\sqrt3)$"
t_P: "P(\fgcolor{red}{" + (LaTeX[x(P)]) + "},\fgcolor{669900}{" + (LaTeX[y(P)]) + "})"
text08: "$sin120°≈\frac{\fgcolor{669900}{" + (LaTeX[a]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=\frac{\sqrt3}{2}$
$cos120°≈\frac{\fgcolor{red}{-" + (LaTeX[b]) + "}}{\fgcolor{blue}{" + (LaTeX[c]) + "}}=-\frac{1}{2}$
$tan120°≈\frac{\fgcolor{669900}" + (LaTeX[a]) + "}{\fgcolor{red}{-" + (LaTeX[b]) + "}}=-\sqrt3$"