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3) If \( \sin \theta=0 \), find all values of \( \theta \) where \( 0^{\circ} \leq \theta \leq 360^{\circ} \). I

Ask by King Macdonald. in the United States
Feb 19,2025

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The angles where sin θ = 0 between 0° and 360° are 0°, 180°, and 360°.

Solución

The sine function equals zero when the angle is 0° or a multiple of 180°. Within the interval 0° ≤ θ ≤ 360°, the angles that satisfy sin θ = 0 are: • θ = 0° • θ = 180° • θ = 360° Thus, the solutions are θ = 0°, 180°, and 360°.

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Bonus Knowledge

When \( \sin \theta = 0 \), it means that the angle \( \theta \) corresponds to the points where the sine function crosses the x-axis on the unit circle. Within the range of \( 0^{\circ} \) to \( 360^{\circ} \), this occurs at \( \theta = 0^{\circ} \) and \( \theta = 180^{\circ} \). To find all values of \( \theta \) where \( \sin \theta = 0 \) in this interval, simply remember that these angles correspond to the horizontal line on the unit circle. Thus, the solution is \( \theta = 0^{\circ}, 180^{\circ} \).

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