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Home » t = \frac{2 \pm \sqrt184}6 - Simpleprint

t = \frac{2 \pm \sqrt184}6 - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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2\sin^2 z - 3\sin z + 1 = 0
Let $x = \sin z$. Then:
2x^2 - 3x + 1 = 0
Solve the quadratic:
x = \frac{3 \pm \sqrt{9 - 8}}{4} = \frac{3 \pm 1}{4} \Rightarrow x = 1...
Now solve for $z$:
$\sin z = 1 \Rightarrow z = 90^\circ$
$\sin z = \frac{1}{2} \Rightarrow z = 30^\circ, 150^\circ$
Thus, the solutions are:
\boxed{30^\circ, 90^\circ, 150^\circ}

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