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

Verified step by step guidance

1. Start with the given equation: \(\frac{\sin \theta}{2} = 0\). This means that \(\sin \theta\) divided by 2 equals zero.
2. Multiply both sides of the equation by 2 to isolate \(\sin \theta\): \(\sin \theta = 0\).
3. Recall that \(\sin \theta = 0\) at specific angles within the interval \([0^\circ, 360^\circ)\), specifically where the sine function crosses the x-axis.
4. 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.
5. Write down the exact solutions for \(\theta\) in degrees within \([0^\circ, 360^\circ)\) where \(\sin \theta = 0\).

Key Concepts

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.