三角比

加法定理

Mathematica で聞く高校数学（和積公式・積和公式）

?Play

Play[Sin[2000 t] + Sin[2010 t], {t, 0, 10}]

Play[Sin[20 t] + Sin[21 t], {t, 0, 10}]

Plot[Sin[20 t] + Sin[21 t], {t, 0, 10}]

Play[Sin[2000 t], {t, 0, 10}]

綱引きの原理

n = 5;

arrows = 
        Table[{Cos[2 Pi k/n], Sin[2 Pi k/n]}, {k, 0, 
            n - 1}];

arrows

points = FoldList[Plus, {0, 0}, arrows];

ListPlot[points, PlotJoined -> True, 
        AspectRatio -> Automatic];

s = Sum[Cos[2 Pi k/n], {k, 0, n - 1}]

N[s]

Expand[s (1 - Cos[2 Pi/n]), Trig -> True]

ListPlot[Flatten[Transpose[{Table[{0, 0}, {n}], arrows}], 1], 
        PlotJoined -> True, AspectRatio -> Automatic];

Transpose[{Table[{0, 0}, {n}], arrows}]

Flatten[Transpose[{Table[{0, 0}, {n}], arrows}], 1]

{{a, b}, {c, d}}

{{a, b}, {c, d}} // MatrixForm

% // Transpose

練習問題

a = Table[Cos[k t], {k, 1, 7}];

b = Table[Sin[k t], {k, 1, 7}];

a*b

ab = Expand[a*b, Trig -> True]

Clear[ab]

ab = TrigReduce[a*b]

Apply[Times, ab]

今日のコマンド

?FoldList

?Expand

?Trig

?TrigExpand

?TrigReduce