Question

find an angle in each quadrant with a common reference angle with 47°, from 0°≤θ<360°

Explanation:

Step1: Quadrant I Angle

In Quadrant I, the angle is equal to its reference angle. So the angle is $47^\circ$.

Step2: Quadrant II Angle

In Quadrant II, the formula is $180^\circ - \text{reference angle}$. So $180^\circ - 47^\circ = 133^\circ$.

Step3: Quadrant III Angle

In Quadrant III, the formula is $180^\circ + \text{reference angle}$. So $180^\circ + 47^\circ = 227^\circ$.

Step4: Quadrant IV Angle

In Quadrant IV, the formula is $360^\circ - \text{reference angle}$. So $360^\circ - 47^\circ = 313^\circ$.

Answer:

Quadrant I: $47^\circ$, Quadrant II: $133^\circ$, Quadrant III: $227^\circ$, Quadrant IV: $313^\circ$