Trigonometrie 2
Trigonmetrische Identitäten bzw. Umrechnungen
Trigonmetrische Identitäten bzw. Umrechnungen
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\(\sin{(\frac{x}{2})}\)
\(\pm \sqrt{\frac{1 - \cos{x}}{2}}\)
\(\cos {(\frac{x}{2})}\)
\(\pm \sqrt{\frac{1 + \cos{x}}{2}}\)
\(\tan{(\frac{x}{2})}\)
\(\pm \sqrt{\frac{1 - \cos{x}}{1+ \cos {x}}} = \frac{\sin {x}}{1+\cos{x}}=\frac{1- \cos{x}}{\sin{x}}\)
\(\sin{(3x})\)
\(3 \cdot \sin{x}-4 \cdot \sin^3{x}\)
\(\cos{(3x})\)
\(4 \cdot \cos^3{x}-3 \cdot \cos{x}\)
\(\tan{(3x})\)
\(\frac{3 \ \cdot \ \tan{x}-\tan^3{x}}{1-3 \ \cdot \ \tan^2 {x}}\)
\(\sin^2{x}\)
\(\frac{1}{2} \cdot \ [1- \cos{(2x})]\)
\(\sin^3{x}\)
\(\frac{1}{4} \cdot \ [3 \cdot \ \sin{x} - \sin{(3x})]\)
\(\sin^4{x}\)
\(\frac{1}{8} \cdot \ [\cos{(4x}) - 4 \ \cdot \ \cos{(2x}) + 3]\)
\(\cos^2{x}\)
\(\frac{1}{2} \cdot \ [1+ \cos{(2x})]\)
\(\cos^3{x}\)
\(\frac{1}{4} \cdot \ [3 \cdot \ \cos{(x}) + \cos{(3x})]\)
\(\cos^4{x}\)
\(\frac{1}{8} \cdot \ [\cos{(4x}) + 4 \ \cdot \ \cos{(2x}) + 3]\)
\(\sin {x_1} + \sin{x_2}\)
\(2 \cdot \ \sin{\left(\frac{x_1 + x_2}{2}\right)} \cdot \cos{\left(\frac{x_1 - x_2}{2}\right)}\)
\(\sin{x_1} - \sin{x_2}\)
\(2 \cdot \ \cos{\left(\frac{x_1 + x_2}{2}\right)} \cdot \sin{\left(\frac{x_1 - x_2}{2}\right)}\)
\(\cos{x_1} + \cos{x_2}\)
\(2 \cdot \ \cos{\left(\frac{x_1 + x_2}{2}\right)} \cdot \cos{\left(\frac{x_1 - x_2}{2}\right)}\)
\(\cos{x_1} - \cos{x_2}\)
\(2 \cdot \ \sin{\left(\frac{x_1 + x_2}{2}\right)} \cdot \sin{\left(\frac{x_1 - x_2}{2}\right)}\)
\(\sin{(x_1 + x_2}) + \sin{(x_1 - x_2})\)
\(2 \cdot \ \sin{x_1} \cdot \ \cos{x_2}\)
\(\sin{(x_1 + x_2}) - \sin{(x_1 - x_2})\)
\(2 \cdot \ \cos{x_1} \cdot \ \sin{x_2}\)
\(\cos{(x_1 + x_2}) + \cos{(x_1 - x_2})\)
\(2 \cdot \ \cos{x_1} \cdot \ \cos{x_2}\)
\(\cos{(x_1 + x_2}) - \cos{(x_1 - x_2})\)
\(2 \cdot \ \sin{x_1} \cdot \ \sin{x_2}\)
\(\sin{x_1} \cdot \ \sin{x_2}\)
\(\frac{1}{2} \cdot \ [\cos{(x_1 -x_2}) - \cos{(x_1 +x_2})]\)
\(\cos{x_1} \cdot \ \cos{x_2}\)
\(\frac{1}{2} \cdot \ [\cos{(x_1 -x_2}) + \cos{(x_1 +x_2})]\)
\(\sin{x_1} \cdot \ \cos{x_2}\)
\(\frac{1}{2} \cdot \ [\sin{(x_1 -x_2}) + \sin{(x_1 +x_2})]\)
\(\tan{x_1} \cdot \ \tan{x_2}\)
\(\frac{\tan{x_1} \ + \ \tan{x_2}}{\cot{x_1} \ + \ \cot{x_2}}\)
\(\text{Darstellung von} \ y = a^x \ \text{durch e-Funktion} \)
\(a^x=e^{\lambda x}=e^{(\ln{a})x}\)
