Question

an angle whose measure is -302° is in standard position. in which quadrant does the terminal side of the angle fall?
quadrant i
quadrant ii
quadrant iii
quadrant iv

Explanation:

Step1: Find a positive coterminal angle

To find a positive coterminal angle of \(-302^{\circ}\), we add \(360^{\circ}\) (since angles that differ by a multiple of \(360^{\circ}\) are coterminal).
\(- 302^{\circ}+360^{\circ}=58^{\circ}\)

Step2: Determine the quadrant

We know that:

• 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 \(0^{\circ}<58^{\circ}<90^{\circ}\), the angle \(58^{\circ}\) (and thus the angle \(-302^{\circ}\)) has its terminal side in Quadrant I.

Answer:

Quadrant I