Wiki-Quellcode von Lösung Tangente in einem Kurvenpunkt III
Version 6.1 von Martin Stern am 2025/10/13 15:07
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| author | version | line-number | content |
|---|---|---|---|
| 1 | 1. | ||
| 2 | [[image:Kosinusfunktion.svg||width="450" style="display:block;margin-left:auto;margin-right:auto"]] | ||
| 3 | |||
| 4 | 2. | ||
| 5 | {{formula}}h(x)=cos(\frac{\pi}{4}x)+1{{/formula}} | ||
| 6 | {{formula}}h'(x)=\frac{\pi}{4}\cdot (-sin(\frac{\pi}{4}x))+1=-\frac{\pi}{4} sin(\frac{\pi}{4}x){{/formula}} | ||
| 7 | {{formula}}h'(6)=-\frac{\pi}{4}sin(\frac{\pi}{4}\cdot 6)=\frac{\pi}{4}{{/formula}} | ||
| 8 | {{formula}}h(6)=1{{/formula}} | ||
| 9 | Einsetzen von {{formula}}m=\frac{\pi}{4}{{/formula}} und {{formula}}P(6|1){{/formula}}in {{formula}}y=mx+c{{/formula}} liefert {{formula}}c=1-\frac{3}{2}\pi{{/formula}}. | ||
| 10 | {{formula}}t: y=\frac{\pi}{4}x+1-\frac{3}{2}\pi{{/formula}} |