Find an angle in each quadrant with a common reference angle with 193°, from 0°≤θ<360°

Sure, let's find the angles in each quadrant that have the same reference angle as 193°.

1. First, we need to find the reference angle. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For an angle of 193°, the reference angle is 180° - 193° = -13°. However, reference angles are always positive, so we take the absolute value to get 13°.

2. Now, we find an angle in each quadrant that has this reference angle:

   • Quadrant I: The angle is simply the reference angle, 13°.

   • Quadrant II: We subtract the reference angle from 180° to get the angle in the second quadrant. So, 180° - 13° = 167°.

   • Quadrant III: We add the reference angle to 180° to get the angle in the third quadrant. So, 180° + 13° = 193°.

   • Quadrant IV: Since angles in the fourth quadrant are between 270° and 360°, we subtract the reference angle from 360°. So, 360° - 13° = 347°.

So, the angles in each quadrant that have the same reference angle as 193° are 13°, 167°, 193°, and 347°.