Hallo !
f(x) = 5 * sin(4 * x - 0.5 * pi) - 3
f´(x) = 20 * cos(0.5 * pi - 4 * x)
Newtonverfahren -->
x _ (n + 1) = x _ n - f(x _ n) / f´(x _ n)
Startwerte - Tabelle -->
-1.6 --> -5.265963355243217
-1.5 --> -1.017221983859334
-1.4 --> -1.017221983859334
-1.3 --> -1.017221983859334
-1.2 --> -1.017221983859334
-1.1 --> -1.017221983859334
-1.0 --> -1.017221983859334
-0.9 --> -1.017221983859334
-0.8 --> -2.58801831065423
-0.7 --> -0.5535743748585278
-0.6 --> -0.5535743748585278
-0.5 --> -0.5535743748585278
-0.4 --> -0.5535743748585278
-0.3 --> -0.5535743748585278
-0.2 --> -0.5535743748585278
-0.1 --> -1.017221983859334
0 --> 6265082.433087618
+0.1 --> +1.01722195193637
+0.2 --> +0.5535743429355626
+0.3 --> +0.5535743429355626
+0.4 --> +0.5535743429355626
+0.5 --> +0.5535743429355626
+0.6 --> +0.5535743429355626
+0.7 --> +0.5535743429355626
+0.8 --> +2.588018278731266
+0.9 --> +1.01722195193637
+1.0 --> +1.01722195193637
+1.1 --> +1.01722195193637
+1.2 --> +1.01722195193637
+1.3 --> +1.01722195193637
+1.4 --> +1.01722195193637
+1.5 --> +1.01722195193637
+1.6 --> +5.265963323320253
Folgende Nullstellen davon liegen zwischen - pi / 2 und + pi / 2 -->
-1.017221983859334 Fehler --> -2.6 * 10 ^ -7
-0.5535743748585278 Fehler --> +2.6 * 10 ^ -7
+0.5535743429355626 Fehler --> -2.6 * 10 ^ -7
+1.01722195193637 Fehler --> +2.6 * 10 ^ -7
Gerundet also -->
-1.0172220
-0.5535744
+0.5535744
+1.0172220
LG Spielkamerad