which pair of angles has congruent values for the sin x° and the cos y°? 42°, 132° 42°, 138° 42°, 48° 42°, 42°
which pair of angles has congruent values for the sin x° and the cos y°? 42°, 132° 42°, 138° 42°, 48° 42°, 42°
Answer
Explanation:
Step1: Recall the co - function identity
The co - function identity states that (\sin x=\cos(90 - x)). We need to check each pair. For a pair ((x,y)), we want to find when (\sin x=\cos y), i.e., (y = 90 - x).
Step2: Check each option
- Option 1: (x = 42^{\circ},y = 132^{\circ}) (\sin42^{\circ}\neq\cos132^{\circ}) since (\cos132^{\circ}=\cos(90 + 42)^{\circ}=-\sin42^{\circ})
- Option 2: (x = 42^{\circ},y = 138^{\circ}) (\sin42^{\circ}\neq\cos138^{\circ}) since (\cos138^{\circ}=\cos(90+48)^{\circ}=-\sin48^{\circ})
- Option 3: (x = 42^{\circ},y = 48^{\circ}) Using the co - function identity (\sin x=\cos(90 - x)), when (x = 42^{\circ}), then (\sin42^{\circ}=\cos(90 - 42)^{\circ}=\cos48^{\circ})
- Option 4: (x = 42^{\circ},y = 42^{\circ}) (\sin42^{\circ}\neq\cos42^{\circ}) (since (\sin42^{\circ}\approx0.6691) and (\cos42^{\circ}\approx0.7431))
Answer:
(42^{\circ},48^{\circ})