Question

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estimate the given rotation within 10 degrees:

Explanation:

Step1: Analyze the position of the terminal side

The terminal side is in Quadrant III. A full - circle rotation is \(360^{\circ}\), and each quadrant is \(90^{\circ}\).

Step2: Estimate the rotation

Starting from the positive \(x\) - axis and rotating clockwise. The angle is more than \(180^{\circ}\) (half - circle). If we assume a rough estimate, since it is in the third quadrant, and considering the position of the terminal side relative to the axes. A \(210^{\circ}\) clockwise rotation (from the positive \(x\) - axis) would place the terminal side in the third quadrant. Another way: If we consider the counter - clockwise rotation, the clockwise rotation \(\theta\) and the counter - clockwise rotation \(\alpha\) satisfy \(\theta=360^{\circ}-\alpha\). A counter - clockwise rotation of \(150^{\circ}\) (since \(180 - 30=150\)) gives a clockwise rotation of \(360 - 150=210^{\circ}\)

Answer:

\(210^{\circ}\)