Solve for exact solutions over the interval [0°, 360°).
sin θ/2 = 0

검증된 단계별 안내

Start with the given equation: \(\frac{\sin \theta}{2} = 0\). This means that \(\sin \theta\) divided by 2 equals zero.

Multiply both sides of the equation by 2 to isolate \(\sin \theta\): \(\sin \theta = 0\).

Recall that \(\sin \theta = 0\) at specific angles within the interval \([0^\circ, 360^\circ)\), specifically where the sine function crosses the x-axis.

Identify the angles where \(\sin \theta = 0\) in the given interval. These are the angles where the terminal side of \(\theta\) lies along the x-axis.

Write down the exact solutions for \(\theta\) in degrees within \([0^\circ, 360^\circ)\) where \(\sin \theta = 0\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solving Basic Trigonometric Equations

To solve equations like sin(θ/2) = 0, identify the angles where the sine function equals zero. Since sine is zero at integer multiples of 180°, set the argument θ/2 equal to these values and solve for θ within the given interval.

Understanding the Domain and Interval Restrictions

The problem restricts θ to the interval [0°, 360°), so solutions must be found only within this range. After solving for θ, verify that each solution lies within the specified interval to ensure validity.

Angle Multiplication and Division in Trigonometric Functions

When the variable is inside the function with a coefficient (like θ/2), adjust the equation accordingly by multiplying or dividing to isolate θ. This step is crucial to correctly find all possible solutions within the interval.

Solve for exact solutions over the interval [0°, 360°).sin θ/2 = 0