Question

score: 2/3 penalty: none find coterminal, reference, and quadrant question video examples for the rotation 1388°, find the coterminal angle from 0° ≤ θ < 360°, the quadrant, and the reference angle. answer attempt 1 out of 2 the coterminal angle is □°, which lies in quadrant, with a reference angle of □°.

Explanation:

Step1: Find coterminal angle

To find the coterminal angle \(\theta\) of \(1388^{\circ}\) with \(0^{\circ}\leq\theta < 360^{\circ}\), use the formula \(\theta = 1388^{\circ}-n\times360^{\circ}\), where \(n\) is an integer.
\(n = \lfloor\frac{1388}{360}
floor= 3\) (since \(3\times360 = 1080\) and \(4\times360=1440>1388\))
\(\theta=1388 - 3\times360=1388 - 1080 = 308^{\circ}\)

Step2: Determine the quadrant

Quadrant I: \(0^{\circ}<\theta<90^{\circ}\); Quadrant II: \(90^{\circ}<\theta<180^{\circ}\); Quadrant III: \(180^{\circ}<\theta<270^{\circ}\); Quadrant IV: \(270^{\circ}<\theta<360^{\circ}\)
Since \(270^{\circ}<308^{\circ}<360^{\circ}\), the angle \(308^{\circ}\) lies in Quadrant IV.

Step3: Calculate the reference angle

For an angle \(\theta\) in Quadrant IV, the reference angle \(\alpha\) is given by \(\alpha = 360^{\circ}-\theta\)
\(\alpha=360 - 308=52^{\circ}\)

Answer:

The coterminal angle is \(308^{\circ}\), which lies in Quadrant IV, with a reference angle of \(52^{\circ}\)