Trigonometric Equations
Solve each equation on the interval \( 0 \leq \theta < 2\pi\).
1. (a) \(1 -\cos \theta = \frac{1}{2} \)
(b) \( 2\sin \theta + \sqrt 3 = 0 \)
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2. (a) \( 2 \cos (2 \theta) +1 =0 \)
(b) \( \sqrt{3} \tan \left(\frac{\theta}{2}\right) - 3 = 0 \)
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3. \( 2 \cos \theta + \sqrt {2} = 0 \)
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4. \( 4\cos^2 \theta - 3 = 0 \)
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5. \( 2\sin^2 \theta - 1 = \sin \theta\)
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6. \( 2\sin^2 \theta + 1 = 3\sin \theta\)
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7. \( 2\cos^2 \theta + 3\sin \theta = 0\)
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8. \( 2\cos^2 \theta + \cos \theta - 1 =0\)
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9. \( \sin (2 \theta) \sin \theta = \cos \theta\)
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10. \( \cos (2\theta) + 3 = 5 \cos \theta \)
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