Find an angle in each quadrant with a common reference angle with 54°, from 0°≤θ<360°
Question
Find an angle in each quadrant with a common reference angle with 54°, from 0°≤θ<360°
Solution
Sure, let's find the angles in each quadrant that have the same reference angle with 54°.
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Quadrant I: The angle in the first quadrant with a reference angle of 54° is simply 54° itself.
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Quadrant II: To find the angle in the second quadrant, we subtract the reference angle from 180°. So, 180° - 54° = 126°.
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Quadrant III: To find the angle in the third quadrant, we add the reference angle to 180°. So, 180° + 54° = 234°.
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Quadrant IV: To find the angle in the fourth quadrant, we subtract the reference angle from 360°. So, 360° - 54° = 306°.
So, the angles in each quadrant that have the same reference angle with 54° are 54°, 126°, 234°, and 306°.
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