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Home » Daher ist der kleinste Primfaktor von 135 \(\boxed3\). - Veritas Home Health

Daher ist der kleinste Primfaktor von 135 \(\boxed3\). - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 R \sin(2z + \alpha) = \sin(2z) + \sqrt{3} \cos(2z)

📌 R \left( \sin(2z)\cos\alpha + \cos(2z)\sin\alpha \right) = R \cos\alpha \sin(2z) + R \sin\alpha \cos(2z)

📌 Matching coefficients:

📌 R \cos\alpha = 1, \quad R \sin\alpha = \sqrt{3}

📌 R^2 = 1^2 + (\sqrt{3})^2 = 4 \Rightarrow R = 2

📌 \cos\alpha = \frac{1}{2}, \quad \sin\alpha = \frac{\sqrt{3}}{2} \Rightarrow \alpha = 60^\circ

📌 So the equation becomes:

📌 \sin(2z + 60^\circ) = 1 \Rightarrow \sin(2z + 60^\circ) = \frac{1}{2}

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Factor each number from 1 to 12:
$2^3$ (from 8),
$3^2$ (from 9),
$11$.
Others: 4 = $2^2$, 6 = $2\cdot3$, 10 = $2\cdot5$, 12 = $2^2\cdot3$. So...
\mathrm{lcm} = 2^3 \cdot 3^2 \cdot 5 \cdot 7 \cdot 11 = 8 \cdot 9 \cdo...
$8 \cdot 9 = 72$,
$72 \cdot 5 = 360$,
$360 \cdot 7 = 2520$,
$2520 \cdot 11 = 27720$.

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