Question

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for the rotation $-58^{\circ}$, find the coterminal angle from $0^{\circ} \leq \theta < 360^{\circ}$, the quadrant, and the reference angle.

answer
attempt 1 out of 2
the coterminal angle is $\square^{\circ}$, which lies in quadrant $\downarrow$, with a reference angle of $\square^{\circ}$.

Explanation:

Step1: Find coterminal angle

To find a coterminal angle of \(-58^\circ\) within \(0^\circ\leq\theta < 360^\circ\), we add \(360^\circ\) to the given angle.
\(-58^\circ+ 360^\circ=302^\circ\)

Step2: Determine the quadrant

Angles between \(270^\circ\) and \(360^\circ\) lie in Quadrant IV. Since \(270^\circ< 302^\circ< 360^\circ\), the angle \(302^\circ\) is in Quadrant IV.

Step3: Find the reference angle

For an angle in Quadrant IV (\(270^\circ<\theta< 360^\circ\)), the reference angle is given by \(360^\circ-\theta\).
Substitute \(\theta = 302^\circ\) into the formula: \(360^\circ - 302^\circ=58^\circ\)

Answer:

The coterminal angle is \(302^\circ\), which lies in Quadrant IV, with a reference angle of \(58^\circ\).