Question

Consider all angles whose reference angle is 45° with terminal sides not in quadrant I. The angles that share the same tangent value as tan(45°) have terminal sides in quadrant:

a) II
b) III
c) IV
d) I

Answer 1

Angles that share the same tangent value as tan(45°), with terminal sides not in quadrant I, have their terminal sides in quadrant III.

Step-by-step explanation:

The student is asking about the tangent function and reference angles in trigonometry. Tan(45°) is equal to 1. When considering all angles with a reference angle of 45°, the terminal sides for angles that share the same tangent value in quadrants other than I, would be in quadrant III. This is because the tangent function is positive in both quadrant I and III, as both sine and cosine functions are either both positive or both negative in these quadrants, which means their quotient (tangent) is positive.