Question

the angle between 0° and 360° that is coterminal with a standard position angle measuring 859° angle is

Explanation:

Step1: Find the number of full - rotation cycles

To find a coterminal angle with \(859^{\circ}\) between \(0^{\circ}\) and \(360^{\circ}\), divide \(859\) by \(360\).

$$n=\lfloor\frac{859}{360} floor = 2$$

Step2: Calculate the coterminal angle

Use the formula \(\theta=\alpha - n\times360^{\circ}\), where \(\alpha = 859^{\circ}\) and \(n = 2\)

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Answer:

\(139\)