Questions: Find the reference angle for -555°.

Solution Steps

To find the reference angle for a given angle, we first need to bring the angle within the range of \(0^\circ\) to \(360^\circ\) by adding or subtracting \(360^\circ\) as necessary. Once the angle is within this range, the reference angle is the acute angle it makes with the x-axis. If the angle is in the second or third quadrant, subtract it from \(180^\circ\). If it's in the fourth quadrant, subtract it from \(360^\circ\).

To find the reference angle for \( -555^\circ \), we first normalize the angle to be within the range of \( 0^\circ \) to \( 360^\circ \). This is done by calculating: \[ -555 \mod 360 = 165^\circ \]

Next, we identify the quadrant in which \( 165^\circ \) lies. Since \( 165^\circ \) is between \( 90^\circ \) and \( 180^\circ \), it is in the second quadrant. The reference angle \( \theta_{\text{ref}} \) is calculated as: \[ \theta_{\text{ref}} = 180^\circ - 165^\circ = 15^\circ \]

Final Answer