Question

4 multiple choice 1 point in which quadrant does the terminal side of a - 265° angle lie? first quadrant third quadrant second quadrant fourth quadrant

Explanation:

Step1: Find a positive coterminal angle

To find the coterminal angle of \(- 265^{\circ}\), we add \(360^{\circ}\) (since angles that are coterminal differ by a multiple of \(360^{\circ}\)).
\(-265^{\circ}+360^{\circ}=95^{\circ}\)

Step2: Determine the quadrant of the coterminal angle

We know that:

• First - quadrant angles: \(0^{\circ}<\theta < 90^{\circ}\)
• Second - quadrant angles: \(90^{\circ}<\theta < 180^{\circ}\)
• Third - quadrant angles: \(180^{\circ}<\theta < 270^{\circ}\)
• Fourth - quadrant angles: \(270^{\circ}<\theta < 360^{\circ}\)

Since \(90^{\circ}<95^{\circ}<180^{\circ}\), the angle \(95^{\circ}\) (and thus the angle \(-265^{\circ}\) which is coterminal with it) lies in the second quadrant.

Answer:

second quadrant