Question $\newline$ Show Examples $\newline$ Find an angle in each quadrant with a common reference angle with $54^{\circ}$ , from $0^{\circ} \leq \theta<360^{\circ}$ $\newline$ Answer Attempt $1$ out of $2$ $\newline$ Quadrant I: Quadrant II: $\newline$ Quadrant III: Quadrant IV: $\newline$ Submit Answer $\newline$ Copyright $92024$ DeltaMath.com All Rights Reserved. Privacy Policy / Terms of Service

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Writing from expanded to exponent form

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Q. Question

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Show Examples

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Find an angle in each quadrant with a common reference angle with

54^{\circ}

, from

0^{\circ} \leq \theta<360^{\circ}

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Answer Attempt

1

out of

2

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Quadrant I: Quadrant II:

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Quadrant III: Quadrant IV:

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Submit Answer

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92024

Identify Reference Angle: Identify the given reference angle and understand that a reference angle is the acute angle formed by the terminal side of an angle and the x-axis. The given reference angle is $54$ degrees.
Angle in Quadrant I: Determine the angle in Quadrant I with the reference angle of $54$ degrees. In Quadrant I, the angle itself is the reference angle. Therefore, the angle in Quadrant I is $54$ degrees.
Angle in Quadrant II: Calculate the angle in Quadrant II that shares the reference angle of $54$ degrees. To find this angle, subtract the reference angle from $180$ degrees, because angles in Quadrant II have their terminal sides in the second quadrant, and the reference angle is measured from the x-axis to the terminal side, moving counterclockwise. $\newline$ $180$ degrees $-$ $54$ degrees $=$ $126$ degrees
Angle in Quadrant III: Determine the angle in Quadrant III that shares the reference angle of $54^\circ$ . For angles in Quadrant III, add $180^\circ$ to the reference angle, since the reference angle is measured from the terminal side to the x-axis, moving clockwise. $180^\circ + 54^\circ = 234^\circ$
Angle in Quadrant IV: Find the angle in Quadrant IV that shares the reference angle of $54^\circ$ . To find this angle, subtract the reference angle from $360^\circ$ , because angles in Quadrant IV have their terminal sides in the fourth quadrant, and the reference angle is measured from the terminal side to the x-axis, moving clockwise. $\newline$ $360^\circ - 54^\circ = 306^\circ$