$Case=%v$

$O$

$θ$

$5$

\left\lbrace \begin{array}{ll} sinθ=? \\;\ cosθ=? \\;\ tanθ=?\\;\cotθ=?\\;\secθ=?\\;\cscθ=? \end{array}  \right.\ 

$Step=%v$

\left\lbrace \begin{array}{ll} sinθ=\frac{3}{5} \ cosθ=\frac{4}{5} \ tanθ=\frac{3}{4}\cotθ=\frac{4}{3}\secθ=\frac{5}{4}\cscθ=\frac{5}{3} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{4}{5} \ cosθ=\frac{3}{5} \ tanθ=\frac{4}{3}\cotθ=\frac{3}{4}\secθ=\frac{5}{3}\cscθ=\frac{5}{4} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{4}{5} \ cosθ=\frac{-3}{5} \ tanθ=\frac{4}{-3}\cotθ=\frac{-3}{4}\secθ=\frac{5}{-3}\cscθ=\frac{5}{4} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{3}{5} \ cosθ=\frac{-4}{5} \ tanθ=\frac{3}{-4}\cotθ=\frac{-4}{3}\secθ=\frac{5}{-4}\cscθ=\frac{5}{3} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{-3}{5} \ cosθ=\frac{-4}{5} \ tanθ=\frac{-3}{-4}=\frac{3}{4}\cotθ=\frac{-4}{-3}=\frac{4}{3}\secθ=\frac{5}{-4}\cscθ=\frac{5}{-3} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{-4}{5} \ cosθ=\frac{-3}{5} \ tanθ=\frac{-4}{-3}=\frac{4}{3}\cotθ=\frac{-3}{-4}=\frac{3}{4}\secθ=\frac{5}{-3}\cscθ=\frac{5}{-4} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{-4}{5} \ cosθ=\frac{3}{5} \ tanθ=\frac{-4}{3}\cotθ=\frac{3}{-4}\secθ=\frac{5}{3}\cscθ=\frac{5}{-4} \end{array}  \right.\ 

\left\lbrace \begin{array}{ll} sinθ=\frac{-3}{5} \ cosθ=\frac{4}{5} \ tanθ=\frac{-3}{4}\cotθ=\frac{4}{-3}\secθ=\frac{5}{4}\cscθ=\frac{5}{-3} \end{array}  \right.\ 

廣義角的三角函數值

n = 0 (slider from 0 to 8, step 1)
P: (If[n ≟ 1 ∨ n ≟ 8, 4, If[n ≟ 2 ∨ n ≟ 7, 3, If[n ≟ 3 ∨ n ≟ 6, -3, If[n ≟ 4 ∨ n ≟ 5, -4]]]], If[n ≟ 1 ∨ n ≟ 4, 3, If[n ≟ 2 ∨ n ≟ 3, 4, If[n ≟ 5 ∨ n ≟ 8, -3, If[n ≟ 6 ∨ n ≟ 7, -4]]]])
A: (x(P), 0)
O = Intersect(x = 0, y = 0)
b = Segment(A, O)
α = Angle((1, 0), O, P)
c = Segment(O, P)
d = Segment(A, P)
t_P: "P" + (LaTeX[P]) + ""
β = Angle(O, A, P)
s = 0 (slider from 0 to 2, step 1)
poly1, p, o, a_1 = Polygon(O, A, P)
B: Corner[4] + (0.1, -1)