Wiki-Quellcode von Lösung Tangente in einem Kurvenpunkt III
Version 6.4 von Dirk Tebbe am 2025/10/13 15:30
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| author | version | line-number | content |
|---|---|---|---|
 |
6.1 | 1 | 1. |
| 2 | [[image:Kosinusfunktion.svg||width="450" style="display:block;margin-left:auto;margin-right:auto"]] | ||
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3.1 | 3 | |
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6.1 | 4 | 2. |
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3.1 | 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}} | ||
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5.1 | 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}} | ||
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6.2 | 11 | |
| 12 | 3. | ||
| 13 | {{formula}}h'(x)=m{{/formula}} | ||
| 14 | {{formula}}-\frac{\pi}{4} sin(\frac{\pi}{4}x)=2{{/formula}} | ||
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6.3 | 15 | {{formula}}sin(\frac{\pi}{4}x)=-\frac{8}{\pi}{{/formula}} |
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6.4 | 16 | Substituiere:{{formula}}\frac{\pi}{4}x=u{{/formula}} |
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6.3 | 17 | {{formula}}sin(u)=-\frac{8}{\pi}{{/formula}} |
| 18 | {{formula}}-\frac{8}{\pi}<-1{{/formula}} | ||
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6.4 | 19 | {{formula}}-\frac{8}{\pi}{{/formula}} liegt somit ausserhalb des Wertebereichs der Sinusfunktion. |
| 20 | Deswegen hat die Gleichung keine Lösung. | ||
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6.3 | 21 |