Question

consider all angles whose reference angle is 45° with terminal sides not in quadrant i. the angles that share the same cosine value as cos 45° have terminal sides in quadrant iv (complete) the angles that share the same sine value as sin(45°) have terminal sides in quadrant dropdown with ii, iii, iv, (none of the quadrants)

Explanation:

Step1: Recall Sine Sign in Quadrants

Sine corresponds to the \( y \)-coordinate. In Quadrant I, \( \sin\theta>0 \); in Quadrant II, \( \sin\theta>0 \); in Quadrant III, \( \sin\theta<0 \); in Quadrant IV, \( \sin\theta<0 \).

Step2: Analyze \( \sin(45^\circ) \)

\( \sin(45^\circ)=\frac{\sqrt{2}}{2}>0 \). We need quadrants where \( \sin\theta = \sin(45^\circ) \) (same positive value) and terminal side not in Quadrant I. Quadrant II has positive \( y \)-coordinate (same as Quadrant I for sine sign), and reference angle \( 45^\circ \) would give angle \( 180^\circ - 45^\circ=135^\circ \), which has terminal side in Quadrant II.

Answer:

II