加法定理を使って sin、cos を再帰的に求める 6 / TI-Nspire の漸化式 seqGen() で表現する

参考: Interface(インターフェース) 2017年10月号, pp.158-159
 
f:id:ti-nspire:20180406124642p:plain

sincos(initθ,δθ,sinδθ,cosδθ,num):=seqGen({θ(n-1)+δθ,sin_(n-1)*cosδθ+cos_(n-1)*sinδθ,cos_(n-1)*cosδθ-sin_(n-1)*sinδθ},n,{θ,sin_,cos_},{1,num},[[0][sin(initθ)][cos(initθ)]])

実行結果:

a:=sincos(0,((π)/(8)),sin(((π)/(8))),cos(((π)/(8))),100)*1.
[[0.,0.39269908169873,0.78539816339745,1.1780972450962,1.5707963267949,1.9634954084936,2.3561944901924,2.7488935718911,3.1415926535898,3.5342917352885,3.9269908169873,4.319689898686,4.7123889803847,5.1050880620834,5.4977871437822,5.8904862254809,6.2831853071796,6.6758843888783,7.0685834705771,7.4612825522758,7.8539816339745,8.2466807156732,8.639379797372,9.0320788790707,9.4247779607694,9.8174770424681,10.210176124167,10.602875205866,10.995574287564,11.388273369263,11.780972450962,12.17367153266,12.566370614359,12.959069696058,13.351768777757,13.744467859455,14.137166941154,14.529866022853,14.922565104552,15.31526418625,15.707963267949,16.100662349648,16.493361431346,16.886060513045,17.278759594744,17.671458676443,18.064157758141,18.45685683984,18.849555921539,19.242255003238,19.634954084936,20.027653166635,20.420352248334,20.813051330032,21.205750411731,21.59844949343,21.991148575129,22.383847656827,22.776546738526,23.169245820225,23.561944901924,23.954643983622,24.347343065321,24.74004214702,25.132741228718,25.525440310417,25.918139392116,26.310838473815,26.703537555513,27.096236637212,27.488935718911,27.881634800609,28.274333882308,28.667032964007,29.059732045706,29.452431127404,29.845130209103,30.237829290802,30.630528372501,31.023227454199,31.415926535898,31.808625617597,32.201324699295,32.594023780994,32.986722862693,33.379421944392,33.77212102609,34.164820107789,34.557519189488,34.950218271187,35.342917352885,35.735616434584,36.128315516283,36.521014597981,36.91371367968,37.306412761379,37.699111843078,38.091810924776,38.484510006475,38.877209088174]
[0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131]
[1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511,0.,−0.38268343236509,−0.70710678118655,−0.92387953251131,−1.,−0.9238795325113,−0.70710678118655,−0.38268343236511,0.,0.38268343236509,0.70710678118655,0.92387953251131,1.,0.9238795325113,0.70710678118655,0.38268343236511]]

.tns (sincos_recur.tns - Google ドライブ)
f:id:ti-nspire:20180406122545p:plain:w500
横軸は θ。