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

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

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\cos 2\theta = 1 - 2\sin^2\theta
- 2\sin^2\theta = \sin \theta
Rearrange into a quadratic in \(\sin \theta\):
2\sin^2\theta + \sin \theta - 1 = 0
Let \( x = \sin \theta \), so:
2x^2 + x - 1 = 0
x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-1)}}{2(2)} = \frac{-1 \pm \sqrt{1 +...
This gives:
x = \frac{2}{4} = \frac{1}{2} \quad \text{or} \quad x = \frac{-4}{4} =...
So, \( \sin \theta = \frac{1}{2} \) or \( \sin \theta = -1 \).

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