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what is a cankle - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 \boxed{(0, 1, 1)}

📌 Question: Find all angles $z \in [0^\circ, 360^\circ]$ satisfying $2\sin^2 z - 3\sin z + 1 = 0$.

📌 Solution: Let $u = \sin z$. The equation becomes $2u^2 - 3u + 1 = 0$. Solving:

📌 u = \frac{3 \pm \sqrt{9 - 8}}{4} = \frac{3 \pm 1}{4} \implies u = 1 \text{ or } u = \frac{1}{2}.

📌 For $\sin z = 1$: $z = 90^\circ$.

📌 For $\sin z = \frac{1}{2}$: $z = 30^\circ, 150^\circ$.

📌 Thus, solutions are $30^\circ, 90^\circ, 150^\circ$.

📌 \boxed{30^\circ}, \boxed{90^\circ}, \boxed{150^\circ}

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