Question

name the quadrant in which the given angle lies.
-760°
choose the correct answer below.
a. quadrant ii
b. the y - axis
c. quadrant iii
d. the x - axis
e. quadrant iv
f. quadrant i

Explanation:

Step1: Find coterminal angle

To find the coterminal angle of \(-760^\circ\), we add multiples of \(360^\circ\) until we get an angle between \(0^\circ\) and \(360^\circ\). Let's calculate:
\(-760^\circ + 3\times360^\circ=-760^\circ + 1080^\circ = 320^\circ\)

Step2: Determine quadrant

Angles between \(270^\circ\) and \(360^\circ\) lie in Quadrant IV. Since \(270^\circ<320^\circ<360^\circ\), \(320^\circ\) (and thus \(-760^\circ\)) lies in Quadrant IV.

Answer:

E. Quadrant IV